A177757 Number of ways to place 4 nonattacking bishops on an n X n toroidal board.

0, 0, 0, 64, 600, 6912, 29400, 132864, 381024, 1139200, 2613600, 6177600, 12269400, 24912384, 44717400, 81636352, 135945600, 229423104, 360561024, 572788800, 859685400, 1301766400, 1881864600, 2740725504, 3840540000

Offset: 1

Author

Vaclav Kotesovec, May 13 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• V. Kotesovec, Non-attacking chess pieces, 6ed, 2013
• Index entries for linear recurrences with constant coefficients, signature (2,6,-14,-14,42,14,-70,0,70,-14,-42,14,14,-6,-2,1).

Crossrefs

Cf. A172127, A177755, A177756.

Programs

Mathematica

CoefficientList[Series[- 8 x^3 (3 x^11 + 122 x^10 + 401 x^9 + 2508 x^8 + 3316 x^7 + 7780 x^6 + 5172 x^5 + 5236 x^4 + 1609 x^3 + 666 x^2 + 59 x + 8)/((x -  1)^9 (x + 1)^7), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)
LinearRecurrence[{2,6,-14,-14,42,14,-70,0,70,-14,-42,14,14,-6,-2,1},{0,0,0,64,600,6912,29400,132864,381024,1139200,2613600,6177600,12269400,24912384,44717400,81636352},50] (* Harvey P. Dale, Nov 05 2016 *)

Formula

a(n) = 1/48*(n-2)^2*n^2*(2n^4 -16n^3 +50n^2 -84n +81 +(6n^2 -36n +63)*(-1)^n).

G.f.: -8x^4*(3x^11 +122x^10 +401x^9 +2508x^8 +3316x^7 +7780x^6 +5172x^5 +5236x^4 +1609x^3 +666x^2 +59x+8)/((x-1)^9*(x+1)^7).