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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)
4

%I M3200 N1294 #38 Oct 04 2024 10:04:12

%S 1,4,1,16,16,120,8,728,92,8,2,840,24,436,10188,128,12,224,8424,312,72,

%T 192,8784,368,56,224,14500,280,10880,240

%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 Mia Müßig, <a href="https://gist.github.com/PhoenixSmaug/0097fb9cbe9624d1633d6c0ad2b3447a">Julia code to compute the sequence</a>

%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,hard,more

%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 by _Vaclav Kotesovec_, Sep 07 2012

%E a(13)-a(15) from _Andrew Howroyd_, Dec 07 2021

%E a(16)-a(30) from _Mia Muessig_, Oct 04 2024