A172261 Number of ways to place 8 nonattacking kings on an 8 X n board.

0, 0, 25, 1847, 162531, 2501726, 21243084, 119138166, 502726650, 1724809105, 5059647669, 13132889249, 30905051345, 67124176002, 136380034610, 261909043488, 479315827404, 841394145399, 1424246670499, 2334919892115

Offset

1,3

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

a(n) = (1048576n^8 -30277632n^7 +406210560n^6 -3319585920n^5 +18136811049n^4 -68048382318n^3 +171628664735n^2 -266425935930n +194935658400)/2520, n>=7.

G.f.: -x^3*(11814*x^12 -80082*x^11 +366204*x^10 -759794*x^9 +1916625*x^8 -283007*x^7 +5337480*x^6 +4589514*x^5 +4426668*x^4 +1103339*x^3 +146808*x^2 +1622*x +25)/(x-1)^9. [Vaclav Kotesovec, Mar 24 2010]

Mathematica

CoefficientList[Series[- x^2 (11814 x^12 - 80082 x^11 + 366204 x^10 - 759794 x^9 + 1916625 x^8 - 283007 x^7 + 5337480 x^6 + 4589514 x^5 + 4426668 x^4 + 1103339 x^3 + 146808 x^2 + 1622 x + 25) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)

Crossrefs

Cf. A172202, A172203, A172204, A172205, A172206.

Sequence in context: A212333 A187404 A370436 * A023113 A322247 A177837

Adjacent sequences: A172258 A172259 A172260 * A172262 A172263 A172264

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 30 2010

Status

approved