A177758 Number of ways to place 5 nonattacking bishops on an n X n toroidal board.

0, 0, 0, 0, 120, 6912, 52920, 466944, 1905120, 8647680, 25613280, 81838080, 198764280, 510478080, 1082161080, 2393997312, 4594961280, 9120190464, 16225246080, 29656350720, 49689816120, 85128088320, 135870624120

Offset

1,5

Links

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

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

Formula

Explicit formula: 1/240*(n-4)^2*(n-2)^2*n^2*(2n^4 -16n^3 +54n^2 -108n+153 +(10n^2 -60n +135)*(-1)^n).

G.f.: -24x^5*(5x^14 +406x^13 +1333x^12 +14880x^11 +24307x^10 +97498x^9 +95187x^8 +175328x^7 +100307x^6 +93018x^5 +28147x^4 +12832x^3 +1589x^2 +278x+5)/((x-1)^11*(x+1)^9).

Mathematica

CoefficientList[Series[- 24 x^4 (5 x^14 + 406 x^13 + 1333 x^12 + 14880 x^11 + 24307 x^10 + 97498 x^9 + 95187 x^8 + 175328 x^7 + 100307 x^6 + 93018 x^5 + 28147 x^4 + 12832 x^3 + 1589 x^2 + 278 x + 5) / ((x - 1)^11 (x + 1)^9), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

Crossrefs

Cf. A172129, A177755, A177756, A177757.

Sequence in context: A003438 A222157 A092710 * A055213 A035190 A240934

Adjacent sequences: A177755 A177756 A177757 * A177759 A177760 A177761

Keyword

nonn,easy

Author

Vaclav Kotesovec, May 13 2010

Status

approved