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)

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

1,2

Comments

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

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

Table of n, a(n) for n=1..30.

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]

Example

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).

Crossrefs

See A002567 for the number of non-isomorphic solutions.

Cf. A002564, A122749, A103315.

Sequence in context: A099394 A269698 A059991 * A334063 A111661 A072651

Adjacent sequences: A002565 A002566 A002567 * A002569 A002570 A002571

Keyword

nonn,hard,more

Author

N. J. A. Sloane

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

Status

approved