

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
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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 groupbased search for solutions of the nqueens problem, Discr. Math., 307 (2007), 25352551.
V. Kotesovec, Nonattacking chess pieces, 6ed, 2013, p. 6263.
Kevin Pratt, ClosedForm Expressions for the nQueens Problem and Related Problems, arXiv:1609.09585 [cs.DM], 2016.
I. Rivin, I. Vardi and P. Zimmermann, The nqueens problem, Amer. Math. Monthly, 101 (1994), 629639.


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



