A172203 Number of ways to place 4 nonattacking kings on a 4 X n board.

0, 0, 9, 79, 454, 1566, 4103, 9009, 17484, 30984, 51221, 80163, 120034, 173314, 242739, 331301, 442248, 579084, 745569, 945719, 1183806, 1464358, 1792159, 2172249, 2609924

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

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

Crossrefs

Cf. A061997, A061990, A172202.

Programs

Mathematica

CoefficientList[Series[- x^2 (68 x^4 - 4 x^3 + 149 x^2 + 34 x + 9) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

Formula

a(n) = (64n^4 - 720n^3 + 3347n^2 - 7569n + 6894)/6, n>=3.

G.f.: -x^3*(68*x^4-4*x^3+149*x^2+34*x+9)/(x-1)^5. - Vaclav Kotesovec, Mar 24 2010