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A002564
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Number of different ways one can attack all squares on an n X n chessboard using the minimal number of queens.
(Formerly M3199 N1293)
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6
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1, 4, 1, 12, 186, 4, 86, 4860, 114, 8, 2, 8, 288
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listen;
history;
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OFFSET
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1,2
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COMMENTS
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Number of distinct solutions to minimal dominating set on queens' graph Q(n). See A002563 for non-isomorphic solutions.
For same problem, but with non-attacking queens, see A002568. - Vaclav Kotesovec, Sep 07 2012
Number of minimum dominating sets in the n X n queen graph. - Eric W. Weisstein, Dec 31 2017
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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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Table of n, a(n) for n=1..13.
Matthew D. Kearse and Peter B. Gibbons, Computational Methods and New Results for Chessboard Problems, Australasian Journal of Combinatorics 23 (2001), 253-284.
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]
Eric Weisstein's World of Mathematics, Minimum Dominating Set
Eric Weisstein's World of Mathematics, Queen Graph
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CROSSREFS
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Cf. A002563, A002568, A182333.
A075458 gives number of queens required. - Sean A. Irvine, Apr 05 2014
Sequence in context: A299523 A157404 A135704 * A287640 A322078 A019428
Adjacent sequences: A002561 A002562 A002563 * A002565 A002566 A002567
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KEYWORD
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nonn,more
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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New name of the sequence from Vaclav Kotesovec, Sep 07 2012
a(9)-a(10) from Vaclav Kotesovec, Sep 07 2012
a(11) from Svyatoslav Starkov, Sep 16 2013
a(12)-a(13) from Sean A. Irvine, Apr 07 2014
Definition edited by N. J. A. Sloane, Dec 25 2017 at the suggestion of Brendan McKay.
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STATUS
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approved
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