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A179426
Number of ways to place 6 nonattacking kings on an n X n toroidal board.
5
0, 0, 0, 0, 0, 10596, 486668, 7063520, 55345356, 299491100, 1263811604, 4455716184, 13701863604, 37823872044, 95648273100, 224887404416, 497181121100, 1042609380588, 2088337713332, 4017815773400, 7459198321428, 13414493857116, 23444476061772, 39928736913120, 66425550447500, 108162598959740, 172697249542932, 270794133842456, 417578468928308, 634036069773900
OFFSET
1,6
LINKS
Index entries for linear recurrences with constant coefficients, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
FORMULA
a(n) = 1/720*n^2*(n^10 -135*n^8 +7525*n^6 -217665*n^4 +3289354*n^2 -20949480), n>=7.
G.f.: 4*x^6*(426*x^13 - 4263*x^12 + 22311*x^11 - 82449*x^10 + 220918*x^9 - 391803*x^8 + 369356*x^7 + 10716*x^6 - 382230*x^5 + 163719*x^4 + 387689*x^3 - 390831*x^2 - 87230*x - 2649)/(x-1)^13.
MATHEMATICA
CoefficientList[Series[4 x^5 (426 x^13 - 4263 x^12 + 22311 x^11 - 82449 x^10 + 220918 x^9 - 391803 x^8 + 369356 x^7 + 10716 x^6 - 382230 x^5 + 163719 x^4 + 387689 x^3 - 390831 x^2 - 87230 x - 2649) / (x - 1)^13, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 01 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jan 07 2011
STATUS
approved