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A061989 Number of ways to place 3 nonattacking queens on a 3 X n board. 19
0, 0, 0, 0, 4, 14, 36, 76, 140, 234, 364, 536, 756, 1030, 1364, 1764, 2236, 2786, 3420, 4144, 4964, 5886, 6916, 8060, 9324, 10714, 12236, 13896, 15700, 17654, 19764, 22036, 24476, 27090, 29884, 32864, 36036, 39406, 42980, 46764, 50764 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

V. Kotesovec, Ways of placing non-attacking queens and kings..., part of "Between chessboard and computer", 1996, pp. 204 - 206.

E. Lucas, Recreations mathematiques I, Albert Blanchard, Paris, 1992, p. 231.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: 2*x^4*(2*x^2-x+2)/(x-1)^4. Recurrence: a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4), n >= 7. Explicit formula (H. Tarry, 1890): a(n)=(n-3)*(n^2-6*n+12), n >= 3.

(4, 14, 36...) is the binomial transform of row 4 of A117937: (4, 10, 12, 6). - Gary W. Adamson, Apr 09 2006

a(n) = 2*A229183(n-3). - R. J. Mathar, Aug 16 2019

MAPLE

A061989 := proc(n)

    if n >= 3 then

        (n-3)*(n^2-6*n+12) ;

    else

        0;

    end if;

end proc:

seq(A061989(n), n=0..30) ; # R. J. Mathar, Aug 16 2019

MATHEMATICA

CoefficientList[Series[2 x^4 (2 x^2 - x + 2) / (x-1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, May 02 2013 *)

CROSSREFS

Cf. A061990.

Essentially the same as A079908.

Cf. A117937.

Sequence in context: A305906 A177110 A213045 * A079908 A038164 A327382

Adjacent sequences:  A061986 A061987 A061988 * A061990 A061991 A061992

KEYWORD

nonn,easy

AUTHOR

Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 29 2001

STATUS

approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)