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%I M3199 N1293 #57 Mar 22 2024 09:19:56
%S 1,4,1,12,186,4,86,4860,114,8,2,8,288,4632
%N Number of different ways one can attack all squares on an n X n chessboard using the minimal number of queens.
%C Number of distinct solutions to minimal dominating set on queens' graph Q(n). See A002563 for non-isomorphic solutions.
%C For same problem, but with non-attacking queens, see A002568. - _Vaclav Kotesovec_, Sep 07 2012
%C Number of minimum dominating sets in the n X n queen graph. - _Eric W. Weisstein_, Dec 31 2017
%D W. Ahrens, Mathematische Unterhaltungen und Spiele, second edition (1910), Vol. 1, p. 301.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andy Huchala, <a href="/A002564/a002564.py.txt">Python program</a>.
%H Matthew D. Kearse and Peter B. Gibbons, <a href="http://ajc.maths.uq.edu.au/pdf/23/ocr-ajc-v23-p253.pdf">Computational Methods and New Results for Chessboard Problems</a>, Australasian Journal of Combinatorics 23 (2001), 253-284.
%H M. A. Sainte-Laguë, <a href="https://eudml.org/doc/192551">Les Réseaux (ou Graphes)</a>, Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1923, 64 pages. See p. 49.
%H M. A. Sainte-Laguë, <a href="/A002560/a002560.pdf">Les Réseaux (ou Graphes)</a>, 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]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QueenGraph.html">Queen Graph</a>
%Y Cf. A002563, A002568, A182333.
%Y A075458 gives number of queens required. - _Sean A. Irvine_, Apr 05 2014
%K nonn,more
%O 1,2
%A _N. J. A. Sloane_
%E New name of the sequence from _Vaclav Kotesovec_, Sep 07 2012
%E a(9)-a(10) from _Vaclav Kotesovec_, Sep 07 2012
%E a(11) from _Svyatoslav Starkov_, Sep 16 2013
%E a(12)-a(13) from _Sean A. Irvine_, Apr 07 2014
%E Definition edited by _N. J. A. Sloane_, Dec 25 2017 at the suggestion of _Brendan McKay_.
%E a(14) from _Andy Huchala_, Mar 13 2024
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