A194650 Number of ways to place 2 nonattacking kings on an n X n cylindrical chessboard.

0, 0, 9, 68, 215, 504, 1001, 1784, 2943, 4580, 6809, 9756, 13559, 18368, 24345, 31664, 40511, 51084, 63593, 78260, 95319, 115016, 137609, 163368, 192575, 225524, 262521, 303884, 349943, 401040, 457529, 519776, 588159, 663068, 744905, 834084, 931031, 1036184

Offset: 1

Author

Vaclav Kotesovec, Aug 31 2011

Keywords

• nonn

Links

• V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Cf. A061995, A179403.

Programs

Mathematica

CoefficientList[Series[x^2*(4*x^4 - 19*x^3 + 35*x^2 - 23*x - 9)/(x - 1)^5, {x, 0, 50}], x] (* Wesley Ivan Hurt, Dec 27 2023 *)

Formula

a(n) = 1/2*n*(n^3 - 9*n + 6), n>=3.

G.f.: x^3*(4*x^4 - 19*x^3 + 35*x^2 - 23*x - 9)/(x-1)^5.