

A002562


Number of ways of placing n nonattacking queens on n X n board (symmetric solutions count only once).
(Formerly M0180 N0068)


13



1, 0, 0, 1, 2, 1, 6, 12, 46, 92, 341, 1787, 9233, 45752, 285053, 1846955, 11977939, 83263591, 621012754, 4878666808, 39333324973, 336376244042, 3029242658210, 28439272956934, 275986683743434, 2789712466510289
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OFFSET

1,5


REFERENCES

J. R. Bitner and E. M. Reingold, Backtrack programming techniques, Commun. ACM, 18 (1975), 651656.
M. A. SainteLaguë, Les Réseaux (ou Graphes), Mémorial des Sciences Mathématiques, Fasc. 18, GauthierVillars, Paris, 1926, p. 47.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 238.


LINKS

Table of n, a(n) for n=1..26.
Thomas Preusser, Queens%40TUDProject
Eric Weisstein's World of Mathematics, Queens Problem.


FORMULA

a(n) = 1/8 * (Q(n) + P(n) + 2 * R(n)), where Q(n) = A000170(n) [all solutions], P(n) = A032522(n) [point symmetric solutions] and R(n) = A033148(n) [rotationally symmetric solutions].


CROSSREFS

Cf. A000170, A032522, A033148.
Sequence in context: A113216 A081064 A128534 * A218492 A136456 A123968
Adjacent sequences: A002559 A002560 A002561 * A002563 A002564 A002565


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

a(17) and a(18) found by Ulrich Schimke in Goettingen, Germany (UlrSchimke(AT)aol.com)
Formula and a(19) to a(23) added by Matthias Engelhardt in Nuremberg, Germany, Jan 23 2000
Added terms calculated from formula. Thomas B. Preusser (thomas.preusser(AT)tudresden.de), Dec 15 2008
Added a(26) derived by formula after recent extension of A000170. Thomas B. Preusser (thomas.preusser(AT)tudresden.de), Jul 12 2009


STATUS

approved



