A172214 Number of ways to place 5 nonattacking knights on a 5 X n board.

1, 28, 259, 1968, 9386, 30842, 82738, 192336, 400277, 763984, 1360797, 2291056, 3681226, 5687022, 8496534, 12333352, 17459691, 24179516, 32841667, 43842984, 57631432, 74709226, 95635956, 121031712, 151580209

Offset

1,2

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) = (625n^5-8250n^4+57235n^3-242778n^2+608440n-705984)/24, n>=8.

G.f.: x * (42*x^12 -52*x^11 -268*x^10 +884*x^9 -268*x^8 -1188*x^7 +2834*x^6 -720*x^5 +918*x^4 +814*x^3 +106*x^2 +22*x +1) / (x-1)^6. - Vaclav Kotesovec, Mar 25 2010

Mathematica

CoefficientList[Series[(42 x^12 - 52 x^11 - 268 x^10 + 884 x^9 - 268 x^8 - 1188 x^7 + 2834 x^6 - 720 x^5 + 918 x^4 + 814 x^3 + 106 x^2 + 22 x + 1) / (x - 1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

Crossrefs

Cf. A172136, A061991, A172212, A172213.

Sequence in context: A225242 A189606 A336294 * A093196 A179098 A223111

Adjacent sequences: A172211 A172212 A172213 * A172215 A172216 A172217

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved