A172205 Number of ways to place 6 nonattacking kings on a 6 X n board.

0, 0, 16, 408, 8544, 62266, 291908, 1021254, 2916232, 7179314, 15790572, 31795390, 59638832, 105546666, 177953044, 287974838, 449932632, 681918370, 1006409660, 1450930734, 2048760064, 2839684634, 3870800868, 5197362214, 6883673384

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) = 2*(162n^6-3240n^5+29160n^4-151830n^3+483798n^2-895085n+749335)/5, n>=5.

G.f.: -2*x^3*(475*x^8-1015*x^7+4398*x^6+194*x^5+10875*x^4+5233*x^3+3012*x^2 +148*x+8)/(x-1)^7. - Vaclav Kotesovec, Mar 24 2010

Mathematica

CoefficientList[Series[-2 x^2 (475 x^8 - 1015 x^7 + 4398 x^6 + 194 x^5 + 10875 x^4 + 5233 x^3 + 3012 x^2 + 148 x + 8) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

Crossrefs

Cf. A172158, A061992, A172202, A172203, A172204.

Sequence in context: A301447 A202733 A261833 * A209362 A338800 A318220

Adjacent sequences: A172202 A172203 A172204 * A172206 A172207 A172208

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved