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A061997 Number of ways to place 4 nonattacking kings on an n X n board. 17
0, 0, 0, 1, 79, 1987, 16834, 85275, 317471, 962089, 2515262, 5882109, 12605095, 25175191, 47443474, 85152487, 146608359, 243516365, 392004286, 613859609, 938008287, 1402264459, 2055382210, 2959442131, 4192607119 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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 (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

G.f.: - x^3*(30*x^8 - 361*x^7 + 1186*x^6 - 1060*x^5 - 1209*x^4 + 1711*x^3 + 1312*x^2 + 70*x + 1)/(x - 1)^9.

Recurrence: a(n) = 9*a(n - 1) - 36*a(n - 2) + 84*a(n - 3) - 126*a(n - 4) + 126*a(n - 5) - 84*a(n - 6) + 36*a(n - 7) - 9*a(n - 8) + a(n - 9), n >= 12.

Explicit formula (K.Fabel and K.Soltsien): a(n) = (n^8 - 54*n^6 + 72*n^5 + 995*n^4 - 2472*n^3 - 5094*n^2 + 21480*n - 17112)/24, n >= 3.

a(n) = A193580(n,4). - R. J. Mathar, Sep 03 2016

MATHEMATICA

CoefficientList[Series[- x^3 (30 x^8 - 361 x^7 + 1186 x^6 - 1060 x^5 - 1209 x^4 + 1711 x^3 + 1312 x^2 + 70 x + 1) / (x-1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 02 2013 *)

CROSSREFS

Cf. A061995, A061996, A061998.

Sequence in context: A194785 A231802 A098104 * A094731 A182347 A293919

Adjacent sequences:  A061994 A061995 A061996 * A061998 A061999 A062000

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 21:01 EST 2018. Contains 318245 sequences. (Running on oeis4.)