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A178140 Number of ways to place 7 nonattacking bishops on an n X n toroidal board. 3
0, 0, 0, 0, 0, 0, 5040, 589824, 6531840, 98304000, 548856000, 3822059520, 14841066240, 67711795200, 208702494000, 726855843840, 1906252508160, 5500708061184, 12796310741760, 32142458880000, 68146033536000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013

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

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Last modified May 17 14:19 EDT 2022. Contains 353746 sequences. (Running on oeis4.)