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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)
23
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: A219629 A262316 A262919 * 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 December 5 05:27 EST 2016. Contains 278761 sequences.