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A061998 Number of ways to place 5 nonattacking kings on an n X n board. 17
0, 0, 0, 0, 0, 1974, 42368, 397014, 2326320, 10087628, 35464464, 106783320, 285336128, 693331146, 1558986816, 3286192514, 6558317232, 12488282352, 22829958032, 40269324564, 68817690624, 114333609854, 185205015936 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Vaclav Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes, part of V. Kotesovec, Between chessboard and computer, 1996, pp. 204 - 206.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

G.f.: 2*x^5*( - 987 - 19768*x^2 - 10327*x - 958*x^8 + 18152*x^3 + 2711*x^4 + 98*x^9 - 1774*x^6 + 2882*x^7 - 5149*x^5)/(x - 1)^11.

Recurrence: a(n) = 11*a(n - 1) - 55*a(n - 2) + 165*a(n - 3) - 330*a(n - 4) + 462*a(n - 5) - 462*a(n - 6) + 330*a(n - 7) - 165*a(n - 8) + 55*a(n - 9) - 11*a(n - 10) + a(n - 11), n >= 15.

Explicit formula (V.Kotesovec, 1992): a(n) = (n - 4)*(n^9 + 4*n^8 - 74*n^7 - 176*n^6 + 2411*n^5 + 1844*n^4 - 38194*n^3 + 18944*n^2 + 236520*n - 316320)/120, n >= 4.

a(n) = A193580(n,5). - R. J. Mathar, Sep 03 2016

MATHEMATICA

CoefficientList[Series[2 x^5 (-987 - 19768 x^2 - 10327 x - 958 x^8 + 18152 x^3 + 2711 x^4 + 98 x^9 - 1774 x^6 + 2882 x^7 - 5149 x^5) / (x-1)^11, {x, 0, 45}], x] (* Vincenzo Librandi, May 02 2013 *)

CROSSREFS

Cf. A061995, A061996, A061997.

Sequence in context: A135844 A135845 A121995 * A205653 A206182 A205364

Adjacent sequences:  A061995 A061996 A061997 * A061999 A062000 A062001

KEYWORD

nonn,easy

AUTHOR

Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 31 2001

STATUS

approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)