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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)
+0
14
1, 0, 10, 28, 0, 88, 4524, 0, 140692, 820496, 0, 128850048, 1957725000, 0, 605917055356, 13404947681712, 0 (list; graph; listen)
OFFSET

0,3

COMMENT

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 (jvospost3(AT)gmail.com), Feb 20 2005

REFERENCES

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

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.

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

LINKS

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

CROSSREFS

Cf. A051906.

Sequence in context: A103135 A008468 A119548 this_sequence A022422 A113962 A031105

Adjacent sequences: A007702 A007703 A007704 this_sequence A007706 A007707 A007708

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

Two more terms from Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de), Dec 17 1999 and Jan 11 2001

13404947681712 from Matthias Engelhardt (Matthias.R.Engelhardt(AT)web.de), May 01 2005

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Last modified November 22 15:28 EST 2009. Contains 167310 sequences.


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