A172533 Number of ways to place 6 nonattacking knights on an n X n toroidal board.

0, 0, 0, 56, 0, 54972, 764596, 8972896, 62560728, 322246800, 1323868260, 4595943336, 14000143196, 38413461800, 96746410800, 226834407552, 500492572112, 1048044384360, 2096986629308, 4031211268200

Offset

1,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Formula

a(n) = n^2*(n^10-135n^8+8005n^6-262665n^4+4816354n^2-39858840)/720, n>=13.

G.f.: 4*x^4*(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. - Vaclav Kotesovec, Mar 25 2010

Mathematica

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 *)

Crossrefs

Cf. A172529, A172530, A172531, A172532.

Sequence in context: A115410 A250489 A308097 * A206786 A036197 A182355

Adjacent sequences: A172530 A172531 A172532 * A172534 A172535 A172536

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 06 2010

Status

approved