A179425 Number of ways to place 5 nonattacking kings on an n X n toroidal board.

0, 0, 0, 0, 10, 14940, 229908, 1678336, 8155404, 30614620, 96011322, 263506752, 652150382, 1485650012, 3161648520, 6355083264, 12167739256, 22339050588, 39536586430, 67748508480, 112804636266, 183057635420, 290261282204, 450688785408, 686540794500, 1027700020828, 1513897376994, 2197363228480, 3146046781446, 4447496831580

Offset

1,5

Links

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

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Formula

Explicit formula: a(n) = 1/120*n^2*(n^8-90n^6+3155n^4-51450n^2+332544), n>=6.

G.f.: -2x^5*(260x^11 - 1932x^10 + 6567x^9 - 16223x^8 + 38507x^7 - 77869x^6 + 102208x^5 - 61576x^4 - 15301x^3 + 33059x^2 + 7415x + 5)/(x-1)^11.

Mathematica

CoefficientList[Series[- 2 x^4 (260 x^11 - 1932 x^10 + 6567 x^9 - 16223 x^8 + 38507 x^7 - 77869 x^6 + 102208 x^5 - 61576 x^4 - 15301 x^3 + 33059 x^2 + 7415 x + 5) / (x - 1)^11, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 01 2013 *)

Crossrefs

Cf. A061998, A179403, A179404, A179424.

Sequence in context: A229229 A190946 A052498 * A203466 A203695 A181017

Adjacent sequences: A179422 A179423 A179424 * A179426 A179427 A179428

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 07 2011

Status

approved