A035291 Number of ways to place a non-attacking white and black queen on n X n chessboard.

0, 0, 16, 88, 280, 680, 1400, 2576, 4368, 6960, 10560, 15400, 21736, 29848, 40040, 52640, 68000, 86496, 108528, 134520, 164920, 200200, 240856, 287408, 340400, 400400, 468000, 543816, 628488, 722680, 827080, 942400, 1069376, 1208768

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• easy

Examples

			There are 16 ways of putting distinct queens on 3 X 3 so that neither can capture the other.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Programs

Magma

[(3*n^4-10*n^3+9*n^2-2*n)/3: n in [1..40]]; // Vincenzo Librandi, Apr 22 2012

Magma

I:=[0, 0, 16, 88,280]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Apr 22 2012

Mathematica

CoefficientList[Series[8*x^3*(2+x)/(1-x)^5,{x,0,40}],x] (* Vincenzo Librandi, Apr 22 2012 *)

Formula

a(n) = (3 n^4 - 10 n^3 + 9 n^2 - 2 n)/3.

Equals 4 * A052149(n-1). [N. J. A. Sloane, Feb 20 2005]

G.f.: 8*x^3*(2+x)/(1-x)^5. [Colin Barker, Apr 17 2012]