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Search: id:A002562
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| A002562 |
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Number of ways of placing n nonattacking queens on n X n board (symmetric solutions count only once).
(Formerly M0180 N0068)
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+0
11
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| 1, 0, 0, 1, 2, 1, 6, 12, 46, 92, 341, 1787, 9233, 45752, 285053, 1846955, 11977939, 83263591, 621012754, 4878666808, 39333324973, 336376244042, 3029242658210
(list; graph; listen)
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OFFSET
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1,5
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REFERENCES
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M. A. Sainte-Lagu\"{e}, Les R\'{e}seaux (ou Graphes)}, M\'{e}morial des Sciences Math\'{e}matiques, Fasc. 18, Gauthier-Villars, Paris, 1926, p. 47.
J. R. Bitner and E. M. Reingold, Backtrack programming techniques, Commun. ACM, 18 (1975), 651-656.
M. B. Wells, Elements of Combinatorial Computing. Pergamon, Oxford, 1971, p. 238.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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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].
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CROSSREFS
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Cf. A000170, A032522, A033148.
Adjacent sequences: A002559 A002560 A002561 this_sequence A002563 A002564 A002565
Sequence in context: A113216 A081064 A128534 this_sequence A136456 A123968 A068797
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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EXTENSIONS
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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 Nuernberg, Germany, 2000-01-23 (Matthias.R.Engelhardt(AT)web.de)
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