A007705 - OEIS

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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)

	OFFSET	`0,3`
	COMMENTS	`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`
	REFERENCES	`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.`
	LINKS	`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.`
	CROSSREFS	`Cf. A051906.` `Sequence in context: A179546 A119548 A219629 * A196356 A196359 A184686` `Adjacent sequences: A007702 A007703 A007704 * A007706 A007707 A007708`
	KEYWORD	`nonn,nice,hard`
	AUTHOR	`N. J. A. Sloane.`
	EXTENSIONS	`Two more terms from Matthias Engelhardt, Dec 17 1999 and Jan 11 2001` `13404947681712 from Matthias Engelhardt, May 01 2005`
	STATUS	`approved`

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Last modified April 23 22:11 EDT 2014. Contains 240947 sequences.