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A172532 Number of ways to place 5 nonattacking knights on an n X n toroidal board. 4
0, 0, 0, 128, 120, 30312, 283906, 1872064, 8643186, 31702920, 98179400, 267487920, 659015500, 1496908840, 3179369070, 6382030592, 12207535134, 22396355496, 39617305308, 67860021680 (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

Explicit formula (Vaclav Kotesovec, Jan 31 2010): a(n) = n^2*(n^8-90n^6+3395n^4-64290n^2+522504)/120, n>=10.

G.f.: -2*x^4*(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. - Vaclav Kotesovec, Mar 25 2010

MATHEMATICA

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 *)

CROSSREFS

Cf. A172529, A172530, A172531, A172136.

Sequence in context: A252487 A160638 A188829 * A173779 A187353 A248773

Adjacent sequences:  A172529 A172530 A172531 * A172533 A172534 A172535

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Feb 06 2010

STATUS

approved

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Last modified June 28 03:47 EDT 2017. Contains 288813 sequences.