A179403 Number of ways to place 2 nonattacking kings on an n X n toroidal board.

0, 0, 0, 56, 200, 486, 980, 1760, 2916, 4550, 6776, 9720, 13520, 18326, 24300, 31616, 40460, 51030, 63536, 78200, 95256, 114950, 137540, 163296, 192500, 225446, 262440, 303800, 349856, 400950

Offset: 1

Author

Vaclav Kotesovec, Jan 07 2011

Keywords

• nonn
• easy

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
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Cf. A061995.

Programs

Mathematica

CoefficientList[Series[2 x^3 (x-2) (5 x^2 - 13 x + 14) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 01 2013 *)

Formula

Explicit formula: a(n) = 1/2*n^2*(n-3)*(n+3), n>=3.

G.f.: 2*x^4*(x-2)*(5*x^2 - 13*x + 14)/(x-1)^5.