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A051906 Number of ways of placing n nonattacking queens on an n X n toroidal chessboard. 6
1, 0, 0, 0, 10, 0, 28, 0, 0, 0, 88, 0, 4524, 0, 0, 0, 140692, 0, 820496, 0, 0, 0, 128850048, 0, 1957725000, 0, 0, 0, 605917055356, 0, 13404947681712, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The sequence has been computed up to n = 23 by Rivin, Vardi & Zimmermann, see p. 637 of their paper from 1994. Further terms were calculated by the submitter, Dec 17 1999 and Jan 11 2001.

a(n) is divisible by n.

Only terms indexed by odd numbers coprime to 3 are nonzero, therefore A007705(n) = a(2n+1) is the main entry. - M. F. Hasler, Jul 01 2019

LINKS

Table of n, a(n) for n=1..34.

M. R. Engelhardt, A group-based search for solutions of the n-queens problem, Discr. Math., 307 (2007), 2535-2551.

V. Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 62-63.

Kevin Pratt, Closed-Form Expressions for the n-Queens Problem and Related Problems, arXiv:1609.09585 [cs.DM], 2016.

I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math. Monthly, 101 (1994), 629-639.

CROSSREFS

See A007705, which is the main entry for this sequence.

Sequence in context: A107781 A107772 A087474 * A171809 A167302 A302576

Adjacent sequences:  A051903 A051904 A051905 * A051907 A051908 A051909

KEYWORD

nonn,nice,hard,more

AUTHOR

Matthias Engelhardt, Dec 17 1999

EXTENSIONS

Term a(31) added from A007705 by Vaclav Kotesovec, Aug 25 2012

STATUS

approved

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Last modified July 12 01:17 EDT 2020. Contains 335658 sequences. (Running on oeis4.)