A172204 Number of ways to place 5 nonattacking kings on a 5 X n board.

0, 0, 15, 194, 1974, 9856, 34475, 95466, 224589, 468854, 893646, 1585850, 2656976, 4246284, 6523909, 9693986, 13997775, 19716786, 27175904, 36746514, 48849626, 63959000, 82604271, 105374074, 132919169

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) = (625n^5-9750n^4+66415n^3-247626n^2+504664n-446544)/24, n>=4.

G.f.: x^3*(259*x^6-204*x^5+1294*x^4+622*x^3+1035*x^2+104*x+15)/(x-1)^6. - Vaclav Kotesovec, Mar 24 2010

Mathematica

CoefficientList[Series[x^2 * (259 * x^6 - 204 * x^5 + 1294 * x^4 + 622 * x^3 + 1035 * x^2 + 104 * x + 15)/(x - 1)^6, {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)

Crossrefs

Cf. A061998, A061991, A172202, A172203.

Sequence in context: A006238 A201883 A324357 * A015673 A125472 A098300

Adjacent sequences: A172201 A172202 A172203 * A172205 A172206 A172207

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 29 2010

Status

approved