A172532 Number of ways to place 5 nonattacking knights on an n X n toroidal board.

0, 0, 0, 128, 120, 30312, 283906, 1872064, 8643186, 31702920, 98179400, 267487920, 659015500, 1496908840, 3179369070, 6382030592, 12207535134, 22396355496, 39617305308, 67860021680

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^8 - 90*n^6 + 3395*n^4 - 64290*n^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: A160638 A188829 A336776 * A173779 A187353 A248773

Adjacent sequences: A172529 A172530 A172531 * A172533 A172534 A172535

Keyword

nonn,easy

Author

Vaclav Kotesovec, Feb 06 2010

Status

approved