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A194651
Number of ways to place 3 nonattacking kings on an n X n cylindrical chessboard.
3
0, 0, 0, 88, 785, 3528, 11151, 28560, 63513, 127520, 236863, 413736, 687505, 1096088, 1687455, 2521248, 3670521, 5223600, 7286063, 9982840, 13460433, 17889256, 23466095, 30416688, 38998425, 49503168, 62260191, 77639240, 96053713, 117963960, 143880703
OFFSET
1,4
FORMULA
a(n) = 1/6*n*(n^5 - 27*n^3 + 18*n^2 + 194*n - 228), n>=4.
G.f.: -x^4*(15*x^6 - 89*x^5 + 196*x^4 - 140*x^3 - 119*x^2 + 169*x + 88)/(x-1)^7.
MATHEMATICA
CoefficientList[Series[-x^3*(15*x^6 - 89*x^5 + 196*x^4 - 140*x^3 - 119*x^2 + 169*x + 88)/(x - 1)^7, {x, 0, 30}], x] (* Wesley Ivan Hurt, Dec 27 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 31 2011
STATUS
approved