A002566 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.

0, 6, 20, 12, 70, 960, 22, 352, 10, 216, 4814, 72

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

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

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

In other words, the number of minimum total dominating sets in the n X n queen graph. - Eric W. Weisstein, Apr 19 2018

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

• 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]
• Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.
• Eric Weisstein's World of Mathematics, Queen Graph.

Crossrefs

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

Extensions

a(6) corrected and a(9)-a(11) by Sean A. Irvine, Apr 05 2014

Better name from Sean A. Irvine, Apr 05 2014

a(12) from Eric W. Weisstein, Apr 05 2025