A178140 Number of ways to place 7 nonattacking bishops on an n X n toroidal board.

0, 0, 0, 0, 0, 0, 5040, 589824, 6531840, 98304000, 548856000, 3822059520, 14841066240, 67711795200, 208702494000, 726855843840, 1906252508160, 5500708061184, 12796310741760, 32142458880000, 68146033536000

Offset

1,7

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, 12, -26, -65, 156, 208, -572, -429, 1430, 572, -2574, -429, 3432, 0, -3432, 429, 2574, -572, -1430, 429, 572, -208, -156, 65, 26, -12, -2, 1).

Formula

Explicit formula (Vaclav Kotesovec, May 21 2010): (1/10080)*(n-6)^2*(n-4)^2*(n-2)^2*(n^2) * (2*n^6 -36*n^5 +275*n^4 -1224*n^3 +3887*n^2 -9570*n +14625 +(21*n^4 -336*n^3 +2289*n^2 -8190*n +14175)*(-1)^n).

G.f.: -48*x^7 * (105*x^20 +32558*x^19 +69284*x^18 +2532234*x^17 +4270573*x^16 +43976860*x^15 +59687712*x^14 +262529316*x^13 +264238506*x^12 +619225992*x^11 +438942840*x^10 +606753672*x^9 +289183146*x^8 +243462436*x^7 +72876832*x^6 +36501660*x^5 +6031853*x^4 +1631114*x^3 +110244*x^2 +12078*x +105) / ((x-1)^15*(x+1)^13).

Mathematica

CoefficientList[Series[- 48 x^6 (105 x^20 + 32558 x^19 + 69284 x^18 + 2532234 x^17 + 4270573 x^16 + 43976860 x^15 + 59687712 x^14 + 262529316 x^13 + 264238506 x^12 + 619225992 x^11 + 438942840 x^10 + 606753672 x^9 + 289183146 x^8 + 243462436 x^7 + 72876832 x^6 + 36501660 x^5 + 6031853 x^4 + 1631114 x^3 + 110244 x^2 + 12078 x + 105) / ((x - 1)^15 (x + 1)^13), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

Crossrefs

Cf. A177755, A177756, A177757, A177758, A177759, A176886.

Sequence in context: A246615 A291114 A246218 * A180369 A053876 A158050

Adjacent sequences: A178137 A178138 A178139 * A178141 A178142 A178143

Keyword

nonn,easy

Author

Vaclav Kotesovec, May 21 2010

Status

approved