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A007705
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Number of ways of arranging 2n+1 nonattacking queens on a 2n+1 X 2n+1 toroidal board.
(Formerly M4691)
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23
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1, 0, 10, 28, 0, 88, 4524, 0, 140692, 820496, 0, 128850048, 1957725000, 0, 605917055356, 13404947681712, 0
(list;
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listen;
history;
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OFFSET
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0,3
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COMMENTS
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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
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REFERENCES
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W. Ahrens, Mathematische Unterhaltungen und Spiele, Vol. 1, B. G. Teubner, Leipzig, 1921, pp. 363-374.
R. K. Guy, Unsolved problems in Number Theory, 3rd Edn., Springer, 1994, p. 202 [with extensive bibliography]
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.
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LINKS
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Table of n, a(n) for n=0..16.
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.
I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math. Monthly, 101 (1994), 629-639.
Eric Weisstein's World of Mathematics, Queens Problem.
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CROSSREFS
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Cf. A051906.
Sequence in context: A219629 A262316 A262919 * A196356 A196359 A184686
Adjacent sequences: A007702 A007703 A007704 * A007706 A007707 A007708
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KEYWORD
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nonn,nice,hard
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Two more terms from Matthias Engelhardt, Dec 17 1999 and Jan 11 2001
13404947681712 from Matthias Engelhardt, May 01 2005
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STATUS
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approved
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