1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
+-----------------------------------------------------------------------------------------------
0: 20 135 382 454 194 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1: 0 55 574 1818 2028 641 54 0 0 0 0 0 0 0 0 0 0 0 0 0
2: 0 0 136 1508 4412 4025 848 36 0 0 0 0 0 0 0 0 0 0 0 0
3: 0 0 48 771 4286 8095 4422 507 8 0 0 0 0 0 0 0 0 0 0 0
4: 0 0 0 214 2682 9723 11294 2897 156 0 0 0 0 0 0 0 0 0 0 0
5: 0 0 0 68 1214 7423 15392 9437 904 22 0 0 0 0 0 0 0 0 0 0
6: 0 0 0 12 518 4971 16188 17428 4388 141 0 0 0 0 0 0 0 0 0 0
7: 0 0 0 0 96 2126 12632 23044 11162 811 12 0 0 0 0 0 0 0 0 0
8: 0 0 0 0 74 1194 8036 22734 20204 3505 56 0 0 0 0 0 0 0 0 0
9: 0 0 0 0 0 334 4724 19072 26812 9007 366 1 0 0 0 0 0 0 0 0
10: 0 0 0 0 0 160 2314 13374 27880 17054 1590 12 0 0 0 0 0 0 0 0
11: 0 0 0 0 0 41 1016 8563 25010 24283 4668 74 0 0 0 0 0 0 0 0
12: 0 0 0 0 0 0 420 4681 19756 28172 10038 370 0 0 0 0 0 0 0 0
13: 0 0 0 0 0 0 144 2470 13560 27466 16114 1382 6 0 0 0 0 0 0 0
14: 0 0 0 0 0 0 36 1106 8712 24137 21590 3582 38 0 0 0 0 0 0 0
15: 0 0 0 0 0 0 0 408 4926 18595 23766 7147 176 0 0 0 0 0 0 0
16: 0 0 0 0 0 0 0 182 2532 13211 23460 11304 650 0 0 0 0 0 0 0
17: 0 0 0 0 0 0 0 31 1258 8532 20486 14783 1670 10 0 0 0 0 0 0
18: 0 0 0 0 0 0 0 0 450 4904 16172 16816 3590 39 0 0 0 0 0 0
19: 0 0 0 0 0 0 0 0 208 2835 11934 17014 5648 147 0 0 0 0 0 0
20: 0 0 0 0 0 0 0 0 34 1218 7664 15252 8058 482 0 0 0 0 0 0
21: 0 0 0 0 0 0 0 0 0 617 5048 12621 9482 1100 6 0 0 0 0 0
22: 0 0 0 0 0 0 0 0 0 196 2616 9588 10170 2069 10 0 0 0 0 0
23: 0 0 0 0 0 0 0 0 0 50 1446 6650 9798 3058 62 0 0 0 0 0
24: 0 0 0 0 0 0 0 0 0 0 644 4370 8328 4165 190 0 0 0 0 0
25: 0 0 0 0 0 0 0 0 0 0 220 2564 6928 4780 428 1 0 0 0 0
26: 0 0 0 0 0 0 0 0 0 0 70 1392 4952 4922 776 0 0 0 0 0
27: 0 0 0 0 0 0 0 0 0 0 0 719 3516 4747 1228 12 0 0 0 0
28: 0 0 0 0 0 0 0 0 0 0 0 236 2146 4009 1588 38 0 0 0 0
29: 0 0 0 0 0 0 0 0 0 0 0 91 1296 3219 1896 96 0 0 0 0
30: 0 0 0 0 0 0 0 0 0 0 0 2 680 2430 1992 176 0 0 0 0
31: 0 0 0 0 0 0 0 0 0 0 0 0 280 1532 1872 366 0 0 0 0
32: 0 0 0 0 0 0 0 0 0 0 0 0 100 1072 1680 407 4 0 0 0
33: 0 0 0 0 0 0 0 0 0 0 0 0 8 565 1316 634 8 0 0 0
34: 0 0 0 0 0 0 0 0 0 0 0 0 0 288 988 544 18 0 0 0
35: 0 0 0 0 0 0 0 0 0 0 0 0 0 110 668 707 72 0 0 0
36: 0 0 0 0 0 0 0 0 0 0 0 0 0 16 432 506 64 0 0 0
37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 240 489 122 0 0 0
38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 104 346 170 0 0 0
39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 232 122 4 0 0
40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 186 186 11 0 0
41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 66 100 0 0 0
42: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 38 114 38 0 0
43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 84 22 0 0
44: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 44 20 0 0
45: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 39 0 0
46: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 10 0 0
47: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 6 0
48: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0
49: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0
50: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0
51: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
52: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
53: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
54: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
55: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
The total number is 1048576. Result match with second method.
And when we add all the PARR's where not all neighbour points are connected,
we get the following table:
The total number is 84024935266353181.
Result match with second method.
The total number is 2976416.
Result match with second method.
And when we add all the PARR's where not all neighbour points are connected,
we get the following table:
The total number is 4147603839035069.
Result match with second method.
The total number is 517646.
And when we add all the PARR's where not all neighbour points are connected,
we get the following table:
The total number is 31111752828628268.
The total number is 2041600.
And when we add all the PARR's where not all neighbour points are connected,
we get the following table:
The total number is 822802321541410.
All the unique PARR configurations (on 9 or fewer points) without restrictions are:
The total number is 17682852.
The unique PARR configurations with no crossing diagonals are:
The total number is 10215753.
The unique PARR configurations where all neighbour points have a connection, are:
The total number is 113346.
The unique PARR configurations where all neighbour points have a connection,
except for crossing diagonal connections where either one or the other is included, are:
The total number is 466446.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
0: 20 190 1140 4845 15504 38760 77520 125970 167960 184756 167960 125970 77520 38760 15504 4845 1140 190 20 1
1: 0 55 990 8415 44880 168300 471240 1021020 1750320 2406690 2674100 2406690 1750320 1021020 471240 168300 44880 8415 990 55
2: 0 0 280 5965 57360 335000 1341200 3925740 8728720 15095080 20592000 22315150 19230640 13114920 6996080 2859500 865200 182680 24040 1485
3: 0 0 48 2547 45018 415932 2408238 9601956 27861834 60885396 102344814 133931226 137083518 109506852 67623738 31674132 10886238 2590860 381690 26235
4: 0 0 0 734 25062 368607 3099054 16899015 64231398 177947539 369621054 585501543 713223170 668527629 478620282 257230197 100536114 26995905 4456090 341055
5: 0 0 0 140 10482 250105 3065592 22912941 114330064 402457075 1035215370 1988926179 2888587682 3182050023 2644858204 1633039515 726606012 220345741 40787074 3478761
6: 0 0 0 12 3262 133883 2425060 24950216 163810492 734079464 2342542166 5468176315 9483766742 12296315123 11881736752 8438513558 4279025680 1466918426 304766518 28989675
7: 0 0 0 0 688 56432 1563240 22374290 194119880 1110181508 4403585756 12510297489 25951221398 39660064424 44611405370 36488127904 21109939474 8189137268 1911331234 202927725
8: 0 0 0 0 74 18165 823658 16747840 193598604 1418772913 7013029490 24295341830 60379583950 108927180170 142825917058 134701349966 89013576656 39115236326 10265684070 1217566350
9: 0 0 0 0 0 4189 351176 10511589 164171260 1551896171 9595410754 40638203542 121234372742 258604168104 395833916224 431025519558 325724105744 162310156167 47946533470 6358402050
10: 0 0 0 0 0 611 118430 5515607 118927804 1464810099 11391101012 59179940748 212443274022 536837483473 960775834340 1209611784503 1046647836146 592100187932 197071279086 29248649430
11: 0 0 0 0 0 41 30392 2395531 73596200 1198379908 11811589342 75624460472 327681845084 983184839633 2061150713728 3004959929815 2981182990868 1916932699344 719655105062 119653565850
12: 0 0 0 0 0 0 5568 846145 38740386 850903080 10741514616 85275761216 447772649622 1599694651720 3936709486176 6657656249552 7584198626044 5550294130433 2353022543586 438729741450
13: 0 0 0 0 0 0 648 236494 17199454 523629181 8583588760 85168660376 544667906034 2324864003369 6733027382248 13234787250042 17340263497828 14463138438279 6932720515070 1451182990950
14: 0 0 0 0 0 0 36 50146 6355346 278150622 6027307636 75500929649 591754716710 3030493210776 10359591658368 23722281051702 35813056335764 34097172767410 18504184590170 4353548972850
15: 0 0 0 0 0 0 0 7536 1917070 126687531 3712513210 59452098683 575487244068 3553998233112 14391473318092 38491850170466 67095794580296 73043048995136 44943519203774 11899700525790
16: 0 0 0 0 0 0 0 709 459050 48994223 1998867820 41562099782 501540445324 3757873239123 18101369285748 56721374001795 114426453827272 142702148723690 99709070618798 29749251314475
17: 0 0 0 0 0 0 0 31 83686 15871668 935716618 25750590332 391769342766 3587296429091 20656661068924 76101935881731 178145189431520 255035810200772 202703280593664 68248282427325
18: 0 0 0 0 0 0 0 0 10862 4226989 377998486 14097533057 274092169482 3093502189244 21417616888748 93147293884366 253773058130840 418021636291040 378635087038490 144079707346575
19: 0 0 0 0 0 0 0 0 888 901355 130438840 6790356049 171477957490 2409620281072 20193439435130 104160106199110 331393873701844 629710161308264 651340154624340 280576272201225
20: 0 0 0 0 0 0 0 0 34 148001 37926678 2860875206 95691812846 1694056522229 17318344072198 106516490377260 397276712265372 873326587014050 1033845512090776 505037289962205
21: 0 0 0 0 0 0 0 0 0 17579 9119494 1046215372 47465745428 1073403094477 13507061941912 99667809214130 437671460411544 1116622332186482 1516552273888212 841728816603675
22: 0 0 0 0 0 0 0 0 0 1346 1766118 328768598 20831930212 611680614083 9573067265756 85344154051190 443418004937280 1317627390393492 2058637217347996 1300853625660225
23: 0 0 0 0 0 0 0 0 0 50 264902 87610880 8041959190 312577046348 6157805166462 66858377433870 413282298431580 1436058765808152 2588656664535700 1866442158555975
24: 0 0 0 0 0 0 0 0 0 0 28894 19450300 2710335858 142703972680 3588347527370 47885889877435 354378158212320 1446314200685796 3017769339540700 2488589544741300
25: 0 0 0 0 0 0 0 0 0 0 2040 3510614 789902996 57930984770 1889756701416 31322380973485 279481945210080 1346378868699150 3263314170046684 3085851035479212
26: 0 0 0 0 0 0 0 0 0 0 70 497337 196652720 20788250513 896640922988 18682400102640 202603898880300 1158451686493320 3274471289679948 3560597348629860
27: 0 0 0 0 0 0 0 0 0 0 0 52393 41158924 6545707173 381817640764 10140751151600 134879476268160 921033249308080 3049212131234444 3824345300380220
28: 0 0 0 0 0 0 0 0 0 0 0 3745 7088818 1791879702 145226044756 4996509827492 82355624320848 676281409986090 2634877279399140 3824345300380220
29: 0 0 0 0 0 0 0 0 0 0 0 151 975256 421473627 49048507672 2227722331682 46043899267464 458232322091710 2112167669212540 3560597348629860
30: 0 0 0 0 0 0 0 0 0 0 0 2 102608 83894754 14602693352 895338041290 23522582712072 286205804689236 1569874934228724 3085851035479212
31: 0 0 0 0 0 0 0 0 0 0 0 0 7704 13849020 3797619424 322860520558 10953001101480 164551412655216 1081046085222268 2488589544741300
32: 0 0 0 0 0 0 0 0 0 0 0 0 364 1843715 852810736 103865270424 4634328777444 86937333092698 689023498241584 1866442158555975
33: 0 0 0 0 0 0 0 0 0 0 0 0 8 190047 162923060 29602059001 1775198696656 42119368708391 405965178727870 1300853625660225
34: 0 0 0 0 0 0 0 0 0 0 0 0 0 14218 25959284 7410074958 612905257384 18665248860392 220768867493020 841728816603675
35: 0 0 0 0 0 0 0 0 0 0 0 0 0 686 3356432 1611681758 189721144286 7543190733932 110604157585986 505037289962205
36: 0 0 0 0 0 0 0 0 0 0 0 0 0 16 338316 300404875 52314227618 2770055085309 50935737373162 280576272201225
37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24940 47128887 12749599724 920398856273 21505199211786 144079707346575
38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1196 6073972 2719793168 275291750994 8298037784270 68248282427325
39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 621442 501709474 73664204180 2915478371370 29749251314475
40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47951 78788656 17502389766 928617758174 11899700525790
41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2565 10318352 3658307995 266733677798 4353548972850
42: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 81 1095410 664866812 68658087014 1451182990950
43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 90460 103500320 15716215790 438729741450
44: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5444 13528949 3169156890 119653565850
45: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 212 1444715 556332326 29248649430
46: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 121082 83737362 6358402050
47: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7472 10591846 1217566350
48: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 302 1095150 202927725
49: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 88900 28989675
50: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5314 3478761
51: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 208 341055
52: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 26235
53: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1485
54: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 55
55: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
No crossings
This table gives the number of all PARR's per number of points (columns)
and per number of connections (rows) where all neighbouring points are connected,
except for crossing diagonal connections where either one or the other is included.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
+-------------------------------------------------------------------------------------------------------------
0: 20 135 382 454 194 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1: 0 55 574 1818 2028 641 54 0 0 0 0 0 0 0 0 0 0 0 0 0
2: 0 0 136 1508 4412 4025 848 36 0 0 0 0 0 0 0 0 0 0 0 0
3: 0 0 48 771 4286 8095 4422 507 8 0 0 0 0 0 0 0 0 0 0 0
4: 0 0 0 214 2682 9723 11294 2897 156 0 0 0 0 0 0 0 0 0 0 0
5: 0 0 0 92 1414 7923 15816 9509 904 22 0 0 0 0 0 0 0 0 0 0
6: 0 0 0 0 466 5237 17312 18456 4476 141 0 0 0 0 0 0 0 0 0 0
7: 0 0 0 0 208 2872 14412 24948 12206 819 12 0 0 0 0 0 0 0 0 0
8: 0 0 0 0 6 1116 10100 27592 22900 3981 56 0 0 0 0 0 0 0 0 0
9: 0 0 0 0 0 510 5960 24510 33216 10991 382 1 0 0 0 0 0 0 0 0
10: 0 0 0 0 0 48 2742 18304 38784 22334 2166 12 0 0 0 0 0 0 0 0
11: 0 0 0 0 0 0 1274 12109 37052 35495 7004 74 0 0 0 0 0 0 0 0
12: 0 0 0 0 0 0 256 6500 30726 46568 15780 682 0 0 0 0 0 0 0 0
13: 0 0 0 0 0 0 0 3180 22508 49074 30114 2722 6 0 0 0 0 0 0 0
14: 0 0 0 0 0 0 0 1000 14266 45043 44274 7870 78 0 0 0 0 0 0 0
15: 0 0 0 0 0 0 0 36 7702 37066 54538 18077 544 0 0 0 0 0 0 0
16: 0 0 0 0 0 0 0 0 3098 27620 56372 32100 2336 0 0 0 0 0 0 0
17: 0 0 0 0 0 0 0 0 384 16966 51982 46999 6914 26 0 0 0 0 0 0
18: 0 0 0 0 0 0 0 0 0 8304 44516 57304 16154 263 0 0 0 0 0 0
19: 0 0 0 0 0 0 0 0 0 2024 32476 60396 28996 1475 0 0 0 0 0 0
20: 0 0 0 0 0 0 0 0 0 64 19368 57878 43662 4524 0 0 0 0 0 0
21: 0 0 0 0 0 0 0 0 0 0 7170 50736 55062 11658 70 0 0 0 0 0
22: 0 0 0 0 0 0 0 0 0 0 776 37408 59762 22691 514 0 0 0 0 0
23: 0 0 0 0 0 0 0 0 0 0 0 19176 61252 35378 2318 0 0 0 0 0
24: 0 0 0 0 0 0 0 0 0 0 0 4384 55994 47120 6872 0 0 0 0 0
25: 0 0 0 0 0 0 0 0 0 0 0 128 39280 55124 14308 81 0 0 0 0
26: 0 0 0 0 0 0 0 0 0 0 0 0 15152 61280 24946 704 0 0 0 0
27: 0 0 0 0 0 0 0 0 0 0 0 0 1600 58592 35548 3140 0 0 0 0
28: 0 0 0 0 0 0 0 0 0 0 0 0 0 34888 46874 6904 0 0 0 0
29: 0 0 0 0 0 0 0 0 0 0 0 0 0 8464 58520 14668 32 0 0 0
30: 0 0 0 0 0 0 0 0 0 0 0 0 0 256 53792 24248 816 0 0 0
31: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24480 35008 2440 0 0 0
32: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2688 51968 7688 0 0 0
33: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 41344 11488 0 0 0
34: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11264 26240 448 0 0
35: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 256 39424 2752 0 0
36: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23552 3968 0 0
37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2048 17664 0 0
38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24576 0 0
39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6144 1536 0
40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10240 0
41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8192 0
42: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4096
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
0: 20 190 1140 4845 15504 38760 77520 125970 167960 184756 167960 125970 77520 38760 15504 4845 1140 190 20 1
1: 0 55 990 8415 44880 168300 471240 1021020 1750320 2406690 2674100 2406690 1750320 1021020 471240 168300 44880 8415 990 55
2: 0 0 280 5953 57168 333560 1334480 3903900 8676304 14998984 20454720 22160710 19093360 13018824 6943664 2837660 858480 181240 23848 1473
3: 0 0 48 2499 44090 407344 2358566 9402848 27277978 59592104 100138038 130998582 134035902 107036384 66076738 30939944 10630766 2529352 372530 25599
4: 0 0 0 662 23202 345994 2930828 16048887 61144762 169616964 352548108 558596841 680444534 637692858 456417172 245212289 95801838 25714072 4242708 324585
5: 0 0 0 92 8482 215352 2718578 20649748 104014972 368245579 950528394 1830055071 2661026546 2933100718 2438377662 1505399642 669616768 202976623 37552438 3201015
6: 0 0 0 0 2022 99242 1936902 20734868 139339902 633449990 2039909196 4789582049 8337635074 10834859618 10483052958 7449627194 3778002282 1294852646 268886976 25559705
7: 0 0 0 0 256 33037 1067670 16539886 150285662 884510828 3573839672 10276764805 21488904622 33012027331 37255819872 30531027950 17680589980 6860592156 1600843434 169855175
8: 0 0 0 0 6 7422 450356 10538333 132091058 1017969522 5198595826 18403695102 46407535828 84542552624 111570482930 105657091470 69989359800 30791612506 8083262940 958311765
9: 0 0 0 0 0 966 140886 5335144 95024964 974156277 6348837386 27851450380 85098239898 184508798211 285559926438 313232723698 237803377624 118809812339 35136422854 4659693035
10: 0 0 0 0 0 48 30744 2111473 55821904 778010306 6553787514 35922652361 133766279624 346675410928 631334770388 804282063988 701326336748 398626360220 133004904504 19755322853
11: 0 0 0 0 0 0 4146 633855 26541030 518179129 5736836700 39701750317 181458308622 565016264366 1215462890024 1803819047542 1811045635858 1173423901704 442453213418 73703836155
12: 0 0 0 0 0 0 256 137089 10048042 286380318 4258721692 37705341693 213373541238 803146705714 2050176872498 3556832672930 4123132844562 3052132079508 1302920964436 243777975309
13: 0 0 0 0 0 0 0 19491 2950672 130085566 2673505660 30789195947 218041931406 999425503010 3043486167124 6197403762944 8320777259496 7054684765347 3416430357150 719140541907
14: 0 0 0 0 0 0 0 1508 644938 47841456 1410996004 21583469299 193794588960 1091243471866 3989093863844 9578318814452 14947893870014 14556290075634 8014941936176 1901463081405
15: 0 0 0 0 0 0 0 36 98018 13928367 620241140 12940770611 149699224782 1046494728692 4625931104632 13167671270428 23982447439656 26908536186780 16887959780706 4524496838179
16: 0 0 0 0 0 0 0 0 9130 3103544 224008110 6596019078 100266751790 881238672870 4751168505236 16131771764353 34447666563324 44691094592730 32058973364292 9720614193955
17: 0 0 0 0 0 0 0 0 384 502044 65188866 2833043880 57996839790 650673450056 4322297807060 17630507220160 44372533072096 66830077375725 54964534145850 18906830723277
18: 0 0 0 0 0 0 0 0 0 53888 14861662 1012807777 28799598496 420118442486 3479915987072 17194034371436 51309789509304 90117061071840 85269507586200 33363360520371
19: 0 0 0 0 0 0 0 0 0 3208 2544546 296285381 12177011852 236237311282 2474967960554 14955947833508 53282747987826 109685135775480 119861219359350 53500976743725
20: 0 0 0 0 0 0 0 0 0 64 305680 69254604 4335660836 115036526628 1550510133768 11588676385157 49679222894354 120555535914480 152801546391900 78058303626555
21: 0 0 0 0 0 0 0 0 0 0 22746 12495720 1280695800 48144644064 852195530534 7982665161322 41552500807056 119645361558525 176740898386050 103702636455525
22: 0 0 0 0 0 0 0 0 0 0 776 1650932 307507414 17145626924 408728214382 4873980198250 31131943199814 107157391741290 185487103283040 125502767053515
23: 0 0 0 0 0 0 0 0 0 0 0 146200 58321516 5127848793 169872936152 2627453128534 20847481311196 86513667497940 176553288323550 138364589845845
24: 0 0 0 0 0 0 0 0 0 0 0 7296 8375006 1265467770 60628972618 1244187375332 12441049622064 62857724203590 152281509017940 138917164933575
25: 0 0 0 0 0 0 0 0 0 0 0 128 851152 251552537 18365651006 514164264098 6591016138776 41006483067105 118862973301410 126919671598521
26: 0 0 0 0 0 0 0 0 0 0 0 0 54128 38917962 4649499756 183895814708 3084789221804 23948346073260 83805133030920 105402262904055
27: 0 0 0 0 0 0 0 0 0 0 0 0 1600 4449200 963566300 56321309950 1267699308366 12473581175800 53243760917678 79439115953833
28: 0 0 0 0 0 0 0 0 0 0 0 0 0 344952 158823762 14568460600 453923099310 5767040870052 30388461553980 54223568712079
29: 0 0 0 0 0 0 0 0 0 0 0 0 0 15376 19960392 3125149692 140249689864 2352965524657 15521347338538 33433386823185
30: 0 0 0 0 0 0 0 0 0 0 0 0 0 256 1788640 542304184 36930162002 841023595198 7061158017968 18561289434015
31: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101152 73477216 8154589728 260948115316 2844528116886 9241603253505
32: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2688 7366720 1477713384 69470761096 1007362453624 4106643801600
33: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 499584 213279456 15631885856 310790135040 1618972188440
34: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19200 23467648 2913937824 82577842944 562099627760
35: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 256 1836544 437702080 18617262144 170307464688
36: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90112 50877824 3491630848 44511668480
37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2048 4291328 530036736 9886513664
38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 233472 62566400 1829436672
39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6144 5387776 274394880
40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 301056 32047104
41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8192 2734080
42: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 151552
43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4096
Second method
The second method I applied involved slicing. These were
generated on September 3, 2015.
Connected
This table gives the number of all PARR's per number of points (columns)
and per number connections (rows), including those with crossing diagonal connections,
where all neighbour points are connected and where all points are connected through
one or more connections.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
+-----------------------------------------------------------------------------------------
0: 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1: 0 55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2: 0 0 136 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3: 0 0 48 347 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4: 0 0 0 214 746 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5: 0 0 0 68 766 1301 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6: 0 0 0 12 418 2027 1766 0 0 0 0 0 0 0 0 0 0 0 0 0
7: 0 0 0 0 96 1556 3882 1662 0 0 0 0 0 0 0 0 0 0 0 0
8: 0 0 0 0 74 750 4138 5210 1040 0 0 0 0 0 0 0 0 0 0 0
9: 0 0 0 0 0 334 2892 7674 4544 297 0 0 0 0 0 0 0 0 0 0
10: 0 0 0 0 0 160 1646 7226 9254 2332 6 0 0 0 0 0 0 0 0 0
11: 0 0 0 0 0 41 830 5225 11610 6859 506 0 0 0 0 0 0 0 0 0
12: 0 0 0 0 0 0 420 3394 10958 11670 2520 8 0 0 0 0 0 0 0 0
13: 0 0 0 0 0 0 144 1982 8780 13904 6408 304 0 0 0 0 0 0 0 0
14: 0 0 0 0 0 0 36 986 6326 14213 10528 1470 2 0 0 0 0 0 0 0
15: 0 0 0 0 0 0 0 408 3974 12599 13408 3647 80 0 0 0 0 0 0 0
16: 0 0 0 0 0 0 0 182 2124 9787 14978 6440 408 0 0 0 0 0 0 0
17: 0 0 0 0 0 0 0 31 1174 6764 14204 9607 1060 8 0 0 0 0 0 0
18: 0 0 0 0 0 0 0 0 450 4250 12340 11574 2484 35 0 0 0 0 0 0
19: 0 0 0 0 0 0 0 0 208 2479 9500 12562 4204 135 0 0 0 0 0 0
20: 0 0 0 0 0 0 0 0 34 1158 6636 11850 6124 404 0 0 0 0 0 0
21: 0 0 0 0 0 0 0 0 0 617 4422 10381 7546 948 6 0 0 0 0 0
22: 0 0 0 0 0 0 0 0 0 196 2428 8106 8314 1773 10 0 0 0 0 0
23: 0 0 0 0 0 0 0 0 0 50 1382 5950 8316 2664 62 0 0 0 0 0
24: 0 0 0 0 0 0 0 0 0 0 644 3970 7174 3669 186 0 0 0 0 0
25: 0 0 0 0 0 0 0 0 0 0 220 2448 6178 4212 414 1 0 0 0 0
26: 0 0 0 0 0 0 0 0 0 0 70 1340 4520 4466 748 0 0 0 0 0
27: 0 0 0 0 0 0 0 0 0 0 0 719 3280 4255 1158 12 0 0 0 0
28: 0 0 0 0 0 0 0 0 0 0 0 236 2074 3757 1492 38 0 0 0 0
29: 0 0 0 0 0 0 0 0 0 0 0 91 1264 2981 1796 96 0 0 0 0
30: 0 0 0 0 0 0 0 0 0 0 0 2 680 2300 1876 176 0 0 0 0
31: 0 0 0 0 0 0 0 0 0 0 0 0 280 1492 1820 366 0 0 0 0
32: 0 0 0 0 0 0 0 0 0 0 0 0 100 1056 1564 396 4 0 0 0
33: 0 0 0 0 0 0 0 0 0 0 0 0 8 565 1288 622 8 0 0 0
34: 0 0 0 0 0 0 0 0 0 0 0 0 0 288 952 536 18 0 0 0
35: 0 0 0 0 0 0 0 0 0 0 0 0 0 110 664 683 72 0 0 0
36: 0 0 0 0 0 0 0 0 0 0 0 0 0 16 432 506 64 0 0 0
37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 240 469 122 0 0 0
38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 104 346 170 0 0 0
39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 232 122 4 0 0
40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 186 182 11 0 0
41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 66 100 0 0 0
42: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 38 114 38 0 0
43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 84 22 0 0
44: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 44 20 0 0
45: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 39 0 0
46: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 10 0 0
47: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 6 0
48: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0
49: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0
50: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0
51: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
52: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
53: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
54: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
55: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
0: 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1: 0 55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2: 0 0 280 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3: 0 0 48 1731 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4: 0 0 0 734 11446 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5: 0 0 0 140 8242 76707 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6: 0 0 0 12 3070 80819 504804 0 0 0 0 0 0 0 0 0 0 0 0 0
7: 0 0 0 0 688 45684 716324 3195147 0 0 0 0 0 0 0 0 0 0 0 0
8: 0 0 0 0 74 17055 550978 5790807 19158284 0 0 0 0 0 0 0 0 0 0 0
9: 0 0 0 0 0 4189 289950 5696530 42767084 107378885 0 0 0 0 0 0 0 0 0 0
10: 0 0 0 0 0 611 109876 3891534 51729468 287551087 555301346 0 0 0 0 0 0 0 0 0
11: 0 0 0 0 0 41 29818 1985790 43755656 416069806 1748407184 2613812932 0 0 0 0 0 0 0 0
12: 0 0 0 0 0 0 5568 772644 28168260 422319655 2965419576 9523974288 11029666090 0 0 0 0 0 0 0
13: 0 0 0 0 0 0 648 228070 14266308 329634951 3532290098 18639311753 45911541360 40985207931 0 0 0 0 0 0
14: 0 0 0 0 0 0 36 49678 5740722 206028550 3254583758 25625328279 102375981388 192806501075 131159801488 0 0 0 0 0
15: 0 0 0 0 0 0 0 7536 1825822 104979305 2426564422 27347371125 160327729446 484721279080 690975003006 350998859857 0 0 0 0
16: 0 0 0 0 0 0 0 709 450542 43832087 1497562894 23775221256 195341384496 855466493059 1941122499558 2054620219255 753346849574 0 0 0
17: 0 0 0 0 0 0 0 31 83314 14938910 773140112 17277904302 194760035294 1176296434129 3825868019592 6400503325181 4866878070010 1214554530192 0 0
18: 0 0 0 0 0 0 0 0 10862 4106905 334844802 10642716090 163406398494 1327793401733 5880497700466 13979209159887 16701417009116 8609029126058 1305156949328 0
19: 0 0 0 0 0 0 0 0 888 891587 121289710 5593897513 117248918534 1267335414339 7437052451942 23822866705673 40151876339814 32358563873032 10097221259440 698512774464
20: 0 0 0 0 0 0 0 0 34 147627 36434018 2513130916 72606796354 1041109997234 7981612351076 33460381820024 75336342005074 85136797208946 41356216220186 5868462472880
21: 0 0 0 0 0 0 0 0 0 17579 8943164 962847311 38978341484 744069688302 7408140781172 39989071378555 116635341985252 174822061994870 118468106595874 26061463099727
22: 0 0 0 0 0 0 0 0 0 1346 1752658 312692893 18160349966 465542465815 6017987124318 41483395716150 153955712064046 296437584008148 264812843079836 80870614707470
23: 0 0 0 0 0 0 0 0 0 50 264402 85210882 7330703214 255789002618 4311018816444 37838821313938 176885546796808 429179612440308 489021141345216 195748679512336
24: 0 0 0 0 0 0 0 0 0 0 28894 19189586 2552848914 123503606318 2735487261336 30606403180007 179331460635980 541977013931315 771825375035048 391483492205329
25: 0 0 0 0 0 0 0 0 0 0 2040 3492254 761578360 52331415274 1540918163806 22073770386456 161918099932176 605560197119250 1064146343529574 669544954835550
26: 0 0 0 0 0 0 0 0 0 0 70 496707 192654764 19395737597 770905352164 14242030490505 131015069002248 604547412841322 1300705353147134 1001290972829373
27: 0 0 0 0 0 0 0 0 0 0 0 52393 40739040 6254909513 342145349620 8234233080498 95395832112158 542958721981966 1423996747305434 1329287985542168
28: 0 0 0 0 0 0 0 0 0 0 0 3745 7058858 1741933992 134362789376 4267437576466 62665906331156 440782276285600 1406527256592072 1583294011422524
29: 0 0 0 0 0 0 0 0 0 0 0 151 974048 414621087 46495780208 1980715711602 37187716361788 324482615823066 1259920115421014 1704845178132546
30: 0 0 0 0 0 0 0 0 0 0 0 2 102592 83175384 14095446848 821698268353 19941403369542 217041818464282 1027250384830932 1668677645624225
31: 0 0 0 0 0 0 0 0 0 0 0 0 7704 13795078 3714058888 303708109269 9656513978090 132050102116468 764233583528826 1490538757372983
32: 0 0 0 0 0 0 0 0 0 0 0 0 364 1841167 841709318 99567881414 4216314459718 73093950136093 519601047872342 1218472427648540
33: 0 0 0 0 0 0 0 0 0 0 0 0 8 189991 161780750 28782213742 1655955605290 36792217089195 323111914923942 913304357535542
34: 0 0 0 0 0 0 0 0 0 0 0 0 0 14218 25873928 7279660278 583058490390 16820626392460 183793400146488 628417757215166
35: 0 0 0 0 0 0 0 0 0 0 0 0 0 686 3352316 1594847510 183234461388 6971291954758 95585020006276 397143897342334
36: 0 0 0 0 0 0 0 0 0 0 0 0 0 16 338220 298710499 51106578290 2612268660949 45400996299934 230518219558580
37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24940 47004115 12560393668 881951231217 19662101167804 122825043274899
38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1196 6067992 2695440556 267095495772 7746093855606 60012364530332
39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 621302 499220718 72153719108 2767716620840 26846843057720
40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47951 78596776 17265431142 893512111412 10973319351896
41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2565 10308092 3627305741 259398882748 4087096978457
42: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 81 1095086 661578164 67325806784 1382541756860
43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 90456 103228880 15508944546 423010745541
44: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5444 13512617 3142078344 116483335979
45: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 212 1444079 553441884 28692126881
46: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 121070 83495174 6274642458
47: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7472 10576902 1206972750
48: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 302 1094546 201832489
49: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 88888 28900773
50: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5314 3473447
51: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 208 340847
52: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 26231
53: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1485
54: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 55
55: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Connected and no crossings
This table gives the number of all PARR's per number of points (columns)
and per number of connections (rows) where all neighbouring points are connected,
except for crossing diagonal connections where either one or the other is included.
Futhermore, all points are connected through one or more connections.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
+--------------------------------------------------------------------------------------------------------
0: 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1: 0 55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2: 0 0 136 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3: 0 0 48 347 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4: 0 0 0 214 746 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5: 0 0 0 92 766 1301 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6: 0 0 0 0 466 2027 1766 0 0 0 0 0 0 0 0 0 0 0 0 0
7: 0 0 0 0 208 1720 3882 1662 0 0 0 0 0 0 0 0 0 0 0 0
8: 0 0 0 0 6 1092 4514 5210 1040 0 0 0 0 0 0 0 0 0 0 0
9: 0 0 0 0 0 510 3856 8294 4544 297 0 0 0 0 0 0 0 0 0 0
10: 0 0 0 0 0 48 2566 9148 9878 2332 6 0 0 0 0 0 0 0 0 0
11: 0 0 0 0 0 0 1274 8241 14474 7187 506 0 0 0 0 0 0 0 0 0
12: 0 0 0 0 0 0 256 5756 16786 14238 2616 8 0 0 0 0 0 0 0 0
13: 0 0 0 0 0 0 0 3180 15800 21526 7624 304 0 0 0 0 0 0 0 0
14: 0 0 0 0 0 0 0 1000 12074 25933 16208 1750 2 0 0 0 0 0 0 0
15: 0 0 0 0 0 0 0 36 7646 26506 25952 5559 80 0 0 0 0 0 0 0
16: 0 0 0 0 0 0 0 0 3098 22952 33436 13430 600 0 0 0 0 0 0 0
17: 0 0 0 0 0 0 0 0 384 16486 37506 24155 2664 8 0 0 0 0 0 0
18: 0 0 0 0 0 0 0 0 0 8304 36912 35324 7306 75 0 0 0 0 0 0
19: 0 0 0 0 0 0 0 0 0 2024 30684 43324 16188 659 0 0 0 0 0 0
20: 0 0 0 0 0 0 0 0 0 64 19336 47846 28362 2368 0 0 0 0 0 0
21: 0 0 0 0 0 0 0 0 0 0 7170 46800 39522 6890 38 0 0 0 0 0
22: 0 0 0 0 0 0 0 0 0 0 776 37152 48834 15331 370 0 0 0 0 0
23: 0 0 0 0 0 0 0 0 0 0 0 19176 55300 26578 1470 0 0 0 0 0
24: 0 0 0 0 0 0 0 0 0 0 0 4384 55098 38112 4616 0 0 0 0 0
25: 0 0 0 0 0 0 0 0 0 0 0 128 39280 48532 11732 81 0 0 0 0
26: 0 0 0 0 0 0 0 0 0 0 0 0 15152 59360 20498 512 0 0 0 0
27: 0 0 0 0 0 0 0 0 0 0 0 0 1600 58592 30812 2628 0 0 0 0
28: 0 0 0 0 0 0 0 0 0 0 0 0 0 34888 44058 6136 0 0 0 0
29: 0 0 0 0 0 0 0 0 0 0 0 0 0 8464 58520 13132 32 0 0 0
30: 0 0 0 0 0 0 0 0 0 0 0 0 0 256 53792 21688 816 0 0 0
31: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24480 35008 2440 0 0 0
32: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2688 51968 6664 0 0 0
33: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 41344 11488 0 0 0
34: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11264 26240 448 0 0
35: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 256 39424 2752 0 0
36: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23552 3968 0 0
37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2048 17664 0 0
38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24576 0 0
39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6144 1536 0
40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10240 0
41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8192 0
42: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4096
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
0: 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1: 0 55 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2: 0 0 280 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3: 0 0 48 1683 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4: 0 0 0 662 10738 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5: 0 0 0 92 7010 68926 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6: 0 0 0 0 2022 65050 431404 0 0 0 0 0 0 0 0 0 0 0 0 0
7: 0 0 0 0 256 29197 544292 2580344 0 0 0 0 0 0 0 0 0 0 0 0
8: 0 0 0 0 6 7332 337222 4139440 14524166 0 0 0 0 0 0 0 0 0 0 0
9: 0 0 0 0 0 966 127194 3315034 28616570 75877913 0 0 0 0 0 0 0 0 0 0
10: 0 0 0 0 0 48 30072 1684167 28406978 179004422 362923658 0 0 0 0 0 0 0 0 0
11: 0 0 0 0 0 0 4146 578633 18306260 213921999 1005307698 1566585275 0 0 0 0 0 0 0 0
12: 0 0 0 0 0 0 256 133761 8305430 168294750 1415455440 5016490573 6005570758 0 0 0 0 0 0 0
13: 0 0 0 0 0 0 0 19491 2710308 95444340 1323805934 8182992354 21947742742 20061354848 0 0 0 0 0 0
14: 0 0 0 0 0 0 0 1508 626842 40389214 906082586 8921137517 40917643730 82772878346 57030968412 0 0 0 0 0
15: 0 0 0 0 0 0 0 36 97586 12820905 473302748 7191222660 51205021688 174370881513 263212182018 133763320998 0 0 0 0
16: 0 0 0 0 0 0 0 0 9130 3002496 191619924 4490951190 47728173620 247332772794 620493546738 685041720246 247766521704 0 0 0
17: 0 0 0 0 0 0 0 0 384 497820 60031480 2219773022 34834629606 262708791837 987009830438 1792085625434 1398169877744 338579200929 0 0
18: 0 0 0 0 0 0 0 0 0 53888 14316774 873945735 20416889346 220202310548 1180279980544 3167909012572 4029502329410 2092068964952 301925803700 0
19: 0 0 0 0 0 0 0 0 0 3208 2512466 272773567 9718223116 149788282522 1120210684494 4221687166342 7854194394280 6599149829668 2030600018182 130899473007
20: 0 0 0 0 0 0 0 0 0 64 305040 66464852 3763109448 83892027754 869548468750 4484302625584 11564281866224 14085211317426 6967449502708 952573320322
21: 0 0 0 0 0 0 0 0 0 0 22746 12290270 1178184710 38908277864 561350300724 3918248006256 13614296053560 22740439049917 16177951416588 3533500266708
22: 0 0 0 0 0 0 0 0 0 0 776 1643948 294091866 14931250214 303935421286 2868605553402 13241728096504 29422991971122 28436948387836 8867062304725
23: 0 0 0 0 0 0 0 0 0 0 0 146200 57144348 4710035985 138370630060 1777943698372 10852213039910 31554056914994 40120332283598 16849342871429
24: 0 0 0 0 0 0 0 0 0 0 0 7296 8316638 1205898948 52852255872 937386226700 7582575807042 28634547003882 47024452839752 25720740061986
25: 0 0 0 0 0 0 0 0 0 0 0 128 850128 245544377 16824505608 420653098790 4545977700024 22272018126075 46782629618830 32666154511061
26: 0 0 0 0 0 0 0 0 0 0 0 0 54128 38538234 4412297312 160178464296 2344429959648 14961186391334 40046736998704 35287151298718
27: 0 0 0 0 0 0 0 0 0 0 0 0 1600 4438000 936612748 51412700530 1039329206090 8713391563548 29747553354234 32887627744327
28: 0 0 0 0 0 0 0 0 0 0 0 0 0 344952 156745922 13762219358 394663928298 4403826535784 19267704818226 26687760312193
29: 0 0 0 0 0 0 0 0 0 0 0 0 0 15376 19868136 3024301492 127536222992 1928455489853 10903965804954 18960808049481
30: 0 0 0 0 0 0 0 0 0 0 0 0 0 256 1787104 533311640 34728646018 728782234320 5390015803194 11827473101223
31: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 101152 72970688 7857361280 236135861028 2321697470374 6481734421075
32: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2688 7353280 1448039144 64979645520 867499916240 3116680764056
33: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 499584 211275232 14985468608 279255670976 1310779739816
34: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19200 23390848 2843071776 76700349440 479726348528
35: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 256 1835520 432177088 17735861568 151673035952
36: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90112 50607488 3389431808 41011678464
37: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2048 4285184 521438720 9355155712
38: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 233472 62099456 1766759680
39: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6144 5375488 269003008
40: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 301056 31746048
41: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8192 2725888
42: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 151552
43: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4096
Unique configurations
The connected configurations still contain many configurations that only
differ with respect to orientation and translation. I worked on a method
for finding these. Below the tables for the various kinds of unique
connected PARR configurations are given. (These were generated on
September 26, 2015.)
1 2 3 4 5 6 7 8 9
+---------------------------------------
0: 1 0 0 0 0 0 0 0 0
1: 0 2 0 0 0 0 0 0 0
2: 0 0 6 0 0 0 0 0 0
3: 0 0 1 40 0 0 0 0 0
4: 0 0 0 15 302 0 0 0 0
5: 0 0 0 4 175 2839 0 0 0
6: 0 0 0 1 60 2427 26621 0 0
7: 0 0 0 0 13 1192 31301 239977 0
8: 0 0 0 0 2 406 20456 372703 1978587
9: 0 0 0 0 0 99 9401 315932 3931302
10: 0 0 0 0 0 16 3214 188166 4218273
11: 0 0 0 0 0 2 802 85034 3166605
12: 0 0 0 0 0 0 145 29745 1815558
13: 0 0 0 0 0 0 17 8044 823089
14: 0 0 0 0 0 0 2 1634 298662
15: 0 0 0 0 0 0 0 243 86328
16: 0 0 0 0 0 0 0 24 19574
17: 0 0 0 0 0 0 0 2 3355
18: 0 0 0 0 0 0 0 0 418
19: 0 0 0 0 0 0 0 0 33
20: 0 0 0 0 0 0 0 0 2
1 2 3 4 5 6 7 8 9
+---------------------------------------
0: 1 0 0 0 0 0 0 0 0
1: 0 2 0 0 0 0 0 0 0
2: 0 0 6 0 0 0 0 0 0
3: 0 0 1 39 0 0 0 0 0
4: 0 0 0 13 291 0 0 0 0
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