A177756 Number of ways to place 3 nonattacking bishops on an n X n toroidal board.

0, 0, 6, 128, 600, 2688, 7350, 19968, 42336, 89600, 163350, 297600, 490776, 809088, 1242150, 1906688, 2774400, 4036608, 5633766, 7862400, 10613400, 14326400, 18818646, 24718848, 31740000

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, 4, -10, -5, 20, 0, -20, 5, 10, -4, -2, 1).

Crossrefs

Cf. A172124, A177755.

Programs

Mathematica

CoefficientList[Series[- 2 x^2 * (3 x^8 + 58 x^7 + 160 x^6 + 518 x^5 + 442 x^4 + 518 x^3 + 160 x^2 + 58 x + 3)/((x - 1)^7 * (x + 1) ^5), {x, 0,1 50}], x] (* Vincenzo Librandi, May 31 2013 *)
LinearRecurrence[{2,4,-10,-5,20,0,-20,5,10,-4,-2,1},{0,0,6,128,600,2688,7350,19968,42336,89600,163350,297600},30] (* Harvey P. Dale, Aug 31 2024 *)

Formula

Explicit formula: 1/12*(n-2)^2*n^2*(2*n^2-4*n+5+3(-1)^n).

G.f.: -2*x^3*(3*x^8+58*x^7+160*x^6+518*x^5+442*x^4+518*x^3+160*x^2+58*x+3)/((x-1)^7*(x+1)^5).