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

1,3

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).

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).

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 *)

Crossrefs

Cf. A172124, A177755.

Sequence in context: A081623 A223210 A324093 * A089314 A111873 A348796

Adjacent sequences: A177753 A177754 A177755 * A177757 A177758 A177759

Keyword

nonn,easy,changed

Author

Vaclav Kotesovec, May 13 2010

Status

approved