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A007705 Number of ways of arranging 2n+1 nonattacking queens on a 2n+1 X 2n+1 toroidal board.
(Formerly M4691)
1, 0, 10, 28, 0, 88, 4524, 0, 140692, 820496, 0, 128850048, 1957725000, 0, 605917055356, 13404947681712, 0 (list; graph; refs; listen; history; text; internal format)



Polya proved [see Ahrens] that the number of solution to this problem for an m X m board is > 0 iff m is coprime to 6. - Jonathan Vos Post, Feb 20 2005


W. Ahrens, Mathematische Unterhaltungen und Spiele, Vol. 1, B. G. Teubner, Leipzig, 1921, pp. 363-374.

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

R. K. Guy, Unsolved problems in Number Theory, 3rd Edn., Springer, 1994, p. 202 [with extensive bibliography]

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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Ilan Vardi, Computational Recreations in Mathematica, Addison-Wesly, 1991, Chapter 6.


Table of n, a(n) for n=0..16.

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

Eric Weisstein's World of Mathematics, Queens Problem.


Cf. A051906.

Sequence in context: A219629 A262316 A262919 * A196356 A196359 A184686

Adjacent sequences:  A007702 A007703 A007704 * A007706 A007707 A007708




N. J. A. Sloane.


Two more terms from Matthias Engelhardt, Dec 17 1999 and Jan 11 2001

13404947681712 from Matthias Engelhardt, May 01 2005



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Last modified February 9 15:42 EST 2016. Contains 268126 sequences.