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Number of ways to attack all squares on an n X n chessboard using the smallest possible number of queens with each queen attacking at least one other.
(Formerly M4130 N1713)
1

%I M4130 N1713 #31 Apr 20 2018 10:02:39

%S 0,6,20,12,70,960,22,352,10,216,4814

%N Number of ways to attack all squares on an n X n chessboard using the smallest possible number of queens with each queen attacking at least one other.

%C Differs from A002564 and A002568 in that each queen is attacking at least one other queen.

%C M. A. Sainte-Laguë paper has "a(6)=900?".

%C In other words, the number of minimum total dominating sets in the n X n queen graph. - _Eric W. Weisstein_, Apr 19 2018

%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 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/QueenGraph.html">Queen Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>

%Y Cf. A002565 (number of ways up to isomorphism).

%K nonn,hard,more

%O 1,2

%A _N. J. A. Sloane_

%E a(6) corrected and a(9)-a(11) by _Sean A. Irvine_, Apr 05 2014

%E Better name from _Sean A. Irvine_, Apr 05 2014