A176886 Number of ways to place 6 nonattacking bishops on an n X n board.

0, 0, 0, 16, 1960, 53744, 692320, 5599888, 33001664, 154215760, 603563504, 2052729728, 6229649352, 17202203680, 43870041520, 104531112928, 234870173248, 501360888160

Offset

1,4

Links

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

Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016

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

Index entries for linear recurrences with constant coefficients, signature (6, -8, -22, 69, -8, -176, 168, 182, -364, 0, 364, -182, -168, 176, 8, -69, 22, 8, -6, 1).

Formula

From Vaclav Kotesovec, Apr 27 2010: (Start)

Explicit formula: a(n) = n*(n-2)*(126*n^10 -2268*n^9 +18774*n^8 -97216*n^7 +361165*n^6 -1029454*n^5 +2283178*n^4 -3841960*n^3 +4676932*n^2 -3808152*n +1640160)/90720 if n is even and a(n) = (n-1)*(n-3)*(126*n^10 -2016*n^9 +14868*n^8 -69244*n^7 +234017*n^6 -607984*n^5 +1211879*n^4 -1797328*n^3 +1953593*n^2 -1550820*n +722925)/90720 if n is odd.

G.f.: -8x^4*(90x^15 +1332x^14 +15417x^13 +93042x^12 +372376x^11 +983864x^10 +1834807x^9 +2423054x^8 +2310242x^7 +1568260x^6 +748519x^5 +239742x^4 +48236x^3 +5264x^2 +233x +2)/((x-1)^13*(x+1)^7). (End)

Mathematica

CoefficientList[Series[- 8 x^3 (90 x^15 + 1332 x^14 + 15417 x^13 + 93042 x^12 + 372376 x^11 + 983864 x^10 + 1834807 x^9 + 2423054 x^8 + 2310242 x^7 + 1568260 x^6 + 748519 x^5 + 239742 x^4 + 48236 x^3 + 5264 x^2 + 233 x + 2) / ((x - 1)^13 (x + 1)^7), {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

Crossrefs

Cf. A172123, A172124, A172127, A172129.

Sequence in context: A167000 A075413 A265213 * A159389 A291828 A086804

Adjacent sequences: A176883 A176884 A176885 * A176887 A176888 A176889

Keyword

nonn,easy

Author

Vaclav Kotesovec, Apr 28 2010

Status

approved