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A002568
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Number of different ways one can attack all squares on an n X n chessboard with the smallest number of non-attacking queens needed.
(Formerly M3200 N1294)
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4
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1, 4, 1, 16, 16, 120, 8, 728, 92, 8, 2, 840, 24, 436, 10188
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OFFSET
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1,2
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COMMENTS
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For same problem, but with queens in general position (without condition "non-attacking"), see A002564. - Vaclav Kotesovec, Sep 07 2012
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REFERENCES
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W. Ahrens, Mathematische Unterhaltungen und Spiele, second edition (1910), Vol. 1, p. 301.
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).
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LINKS
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M. A. Sainte-Laguë, Les Réseaux (ou Graphes), Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1923, 64 pages. See p. 49.
M. A. Sainte-Laguë, Les Réseaux (ou Graphes), Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1923, 64 pages. See p. 49. [Incomplete annotated scan of title page and pages 18-51]
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EXAMPLE
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a(5) = 16 because it is impossible to attack all squares with 2 queens but with 3 queens you can do it in 16 different ways (with mirroring and rotation).
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CROSSREFS
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See A002567 for the number of non-isomorphic solutions.
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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