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

1,4

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

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

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.

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 *)

Crossrefs

Cf. A061995.

Sequence in context: A264303 A200833 A241611 * A158481 A325306 A193428

Adjacent sequences: A179400 A179401 A179402 * A179404 A179405 A179406

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 07 2011

Status

approved