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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
12
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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, 28439272956934, 275986683743434, 2789712466510289
(list; graph; listen)
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OFFSET
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1,5
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REFERENCES
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J. R. Bitner and E. M. Reingold, Backtrack programming techniques, Commun. ACM, 18 (1975), 651-656.
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.
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.
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LINKS
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Thomas Preusser, Queens%40TUD-Project
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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N. J. A. Sloane (njas(AT)research.att.com).
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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)
Added terms calculated from formula. Thomas B. Preusser (thomas.preusser(AT)tu-dresden.de), Dec 15 2008
Added a(26) derived by formula after recent extension of A000170. Thomas B. Preusser (thomas.preusser(AT)tu-dresden.de), Jul 12 2009
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