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A061996 Number of ways to place 3 nonattacking kings on an n X n board. 19
0, 0, 0, 8, 140, 964, 3920, 11860, 29708, 65240, 129984, 240240, 418220, 693308, 1103440, 1696604, 2532460, 3684080, 5239808, 7305240, 10005324, 13486580, 17919440, 23500708, 30456140, 39043144, 49553600, 62316800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

V. Kotesovec, Placing non-attacking queens and kings on boards of various sizes, part of "Between chessboard and computer", 1996, pp. 204 - 206.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

G.f.: - 4*x^3*(2 + 21*x + 38*x^2 - 42*x^3 + 11*x^4)/(x - 1)^7;

Recurrence: a(n) = 7*a(n - 1) - 21*a(n - 2) + 35*a(n - 3) - 35*a(n - 4) + 21*a(n - 5) - 7*a(n - 6) + a(n - 7), n >= 8.

a(n) = (n - 1)*(n - 2)*(n^4 + 3*n^3 - 20*n^2 - 30*n + 132)/6, n >= 1.

a(n) = A193580(n,3). - R. J. Mathar, Sep 03 2016

MATHEMATICA

CoefficientList[Series[-4 x^3 (2 + 21 x + 38 x^2 - 42 x^3 + 11 x^4) / (x-1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, May 02 2013 *)

CROSSREFS

Cf. A061995, A061997, A061998.

Sequence in context: A091060 A092703 A201094 * A234353 A212442 A185248

Adjacent sequences:  A061993 A061994 A061995 * A061997 A061998 A061999

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.)