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A172533 Number of ways to place 6 nonattacking knights on an n X n toroidal board. 2
0, 0, 0, 56, 0, 54972, 764596, 8972896, 62560728, 322246800, 1323868260, 4595943336, 14000143196, 38413461800, 96746410800, 226834407552, 500492572112, 1048044384360, 2096986629308, 4031211268200 (list; graph; refs; listen; history; text; internal format)
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: A201823 A115410 A250489 * A206786 A036197 A182355

Adjacent sequences:  A172530 A172531 A172532 * A172534 A172535 A172536

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Feb 06 2010

STATUS

approved

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Last modified December 17 07:54 EST 2018. Contains 318192 sequences. (Running on oeis4.)