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A002568 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)
4

%I M3200 N1294

%S 1,4,1,16,16,120,8,728,92,8,2,840

%N Number of different ways one can attack all squares on an n X n chessboard with the smallest number of non-attacking queens needed.

%C For same problem, but with queens in general position (without condition "non-attacking"), see A002564. - _Vaclav Kotesovec_, Sep 07 2012

%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]

%e 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).

%Y See A002567 for the number of non-isomorphic solutions.

%Y Cf. A002564, A122749, A103315.

%K nonn

%O 1,2

%A _N. J. A. Sloane_.

%E a(9)-a(12) from _Johan Särnbratt_, Mar 28 2008

%E Name of the sequence corrected, _Vaclav Kotesovec_, Sep 07 2012

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Last modified August 20 10:04 EDT 2019. Contains 326147 sequences. (Running on oeis4.)