A172532
Number of ways to place 5 nonattacking knights on an n X n toroidal board.
Original entry on oeis.org
0, 0, 0, 128, 120, 30312, 283906, 1872064, 8643186, 31702920, 98179400, 267487920, 659015500, 1496908840, 3179369070, 6382030592, 12207535134, 22396355496, 39617305308, 67860021680
Offset: 1
-
CoefficientList[Series[- 2 x^3 (648 x^16 - 10328 x^15 + 71820 x^14 - 295572 x^13 + 818512 x^12 - 1640088 x^11 + 2492742 x^10 - 2967118 x^9 + 2825821 x^8 - 2185007 x^7 + 1376780 x^6 - 677852 x^5 + 219349 x^4 - 32023 x^3 + 18016 x^2 - 644 x + 64) / (x - 1)^11, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)
A172533
Number of ways to place 6 nonattacking knights on an n X n toroidal board.
Original entry on oeis.org
0, 0, 0, 56, 0, 54972, 764596, 8972896, 62560728, 322246800, 1323868260, 4595943336, 14000143196, 38413461800, 96746410800, 226834407552, 500492572112, 1048044384360, 2096986629308, 4031211268200
Offset: 1
-
CoefficientList[Series[4 x^3 (240 x^21 - 3120 x^20 + 20470 x^19 - 105106 x^18 + 512024 x^17 - 2216597 x^16 + 7650408 x^15 - 20251702 x^14 + 41149629 x^13 - 64905350 x^12 + 80399423 x^11 - 78967736 x^10 + 61875645 x^9 - 38631940 x^8 + 19002633 x^7 - 7392461 x^6 + 2560624 x^5 - 840251 x^4 - 8486 x^3 - 14835 x^2 + 182 x - 14) / (x - 1)^13,{x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)
A172966
Number of ways to place 4 nonattacking knights on an n X n cylindrical board.
Original entry on oeis.org
0, 0, 0, 306, 2365, 19047, 90503, 328324, 981693, 2547955, 5933257, 12681288, 25284363, 47595023, 85357395, 146879312, 243867873, 392452803, 614423653, 938708560, 1403123967, 2056426383, 2960698943, 4194107208, 5854060325
Offset: 1
-
CoefficientList[Series[x^3 (76 x^13 - 684 x^12 + 2856 x^11 - 7714 x^10 + 16164 x^9 - 29151 x^8 + 45506 x^7 - 57766 x^6 + 55629 x^5 - 39385 x^4 + 21484 x^3 - 8778 x^2 + 389 x - 306) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)
A173436
Number of ways to place 7 nonattacking knights on an n X n toroidal board.
Original entry on oeis.org
0, 0, 0, 16, 0, 80352, 1359288, 31404480, 339256836, 2527519400, 14053530964, 63100177488, 240356217660, 803630856504, 2416671974700, 6655251717376, 17015566051020, 40822003107000, 92679987456312, 200490192134800
Offset: 1
-
CoefficientList[Series[- 4 x^3 (2535 x^24 - 61497 x^23 + 627330 x^22 - 3849410 x^21 + 16791330 x^20 - 58053150 x^19 + 170691269 x^18 - 438580125 x^17 + 976505385 x^16 - 1844050487 x^15 + 2900976825 x^14 - 3760563305 x^13 + 3991133690 x^12 - 3450574470 x^11 + 2418714751 x^10 - 1370750375 x^9 + 628081926 x^8 - 228075638 x^7 + 56855445 x^6 - 6423333 x^5 + 4868490 x^4 + 36682 x^3 + 20508 x^2 - 60 x + 4) / (x - 1)^15, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)
Showing 1-4 of 4 results.