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A172517 Number of ways to place 2 nonattacking queens on an n X n toroidal board. 9
0, 0, 0, 32, 100, 288, 588, 1152, 1944, 3200, 4840, 7200, 10140, 14112, 18900, 25088, 32368, 41472, 51984, 64800, 79380, 96800, 116380, 139392, 165000, 194688, 227448, 264992, 306124, 352800, 403620, 460800, 522720, 591872, 666400, 749088, 837828 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

FORMULA

a(n) = n^2*(n-2)^2/2 if n is even and a(n) = n^2*(n-1)(n-3)/2 if n is odd.

G.f.: -4*x^4*(x^3+6*x^2+9*x+8) / ((x-1)^5*(x+1)^3). - Colin Barker, Jan 09 2013

MATHEMATICA

CoefficientList[Series[- 4 x^3 (x^3 + 6 x^2 + 9 x + 8) / ((x - 1)^5 (x + 1)^3), {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)

LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 0, 0, 32, 100, 288, 588, 1152}, 40] (* Harvey P. Dale, Sep 22 2015 *)

CROSSREFS

Cf. A007705, A036464.

Sequence in context: A192293 A188862 A228686 * A194645 A134845 A167982

Adjacent sequences:  A172514 A172515 A172516 * A172518 A172519 A172520

KEYWORD

nonn,nice,easy

AUTHOR

Vaclav Kotesovec, Feb 05 2010

STATUS

approved

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Last modified December 18 21:01 EST 2018. Contains 318245 sequences. (Running on oeis4.)