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.

1, 4, 1, 16, 16, 120, 8, 728, 92, 8, 2, 840, 24, 436, 10188, 128, 12, 224, 8424, 312, 72, 192, 8784, 368, 56, 224, 14500, 280, 10880, 240

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

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

Examples

			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).
		

References

• 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).

Links

• Mia Müßig, Julia code to compute the sequence
• 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]

Crossrefs

See A002567 for the number of non-isomorphic solutions.

Cf. A002564, A122749, A103315.

Extensions

a(9)-a(12) from Johan Särnbratt, Mar 28 2008

Name of the sequence corrected by Vaclav Kotesovec, Sep 07 2012

a(13)-a(15) from Andrew Howroyd, Dec 07 2021

a(16)-a(30) from Mia Muessig, Oct 04 2024