

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
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OFFSET

1,4


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
V. Kotesovec, Number of ways of placing nonattacking 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*(n2)^2/2 if n is even and a(n) = n^2*(n1)(n3)/2 if n is odd.
G.f.: 4*x^4*(x^3+6*x^2+9*x+8) / ((x1)^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



