A002564
Number of different ways one can attack all squares on an n X n chessboard using the minimum number of queens.
Original entry on oeis.org
1, 4, 1, 12, 186, 4, 86, 4860, 114, 8, 2, 8, 288, 4632, 205832, 2968, 124, 16, 84
Offset: 1
- 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).
- Andy Huchala, Python program.
- Matthew D. Kearse and Peter B. Gibbons, Computational Methods and New Results for Chessboard Problems, Australasian Journal of Combinatorics 23 (2001), 253-284.
- 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]
- Eric Weisstein's World of Mathematics, Minimal Edge Cover.
- Eric Weisstein's World of Mathematics, Minimum Dominating Set.
- Eric Weisstein's World of Mathematics, Queen Graph.
- Eric W. Weisstein, Symmetrically inequivalent configurations for n = 1 to 7
- Eric W. Weisstein, Symmetrically inequivalent configurations for n = 8
- Eric W. Weisstein, Symmetrically inequivalent configurations for n = 9 to 13
- Eric W. Weisstein, Symmetrically inequivalent configurations for n = 14
- Eric W. Weisstein, Symmetrically inequivalent configurations for n = 16
- Eric W. Weisstein, Symmetrically inequivalent configurations for n = 17 to 19
A002567
Number of nonisomorphic solutions to minimal independent dominating set on queens' graph Q(n).
Original entry on oeis.org
1, 1, 1, 2, 2, 17, 1, 91, 16, 1, 1, 105, 4, 55, 1314, 16, 2, 28
Offset: 1
- 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).
- P. B. Gibbons and J. A. Webb, Some new results for the queens domination problem, Australasian Journal of Combinatorics 15 (1997), pp. 145-160.
- Matthew D. Kearse and Peter B. Gibbons, Computational Methods and New Results for Chessboard Problems, Australasian Journal of Combinatorics 23 (2001), 253-284.
- 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]
See
A002568 for the number of distinct solutions.
A075324 gives number of queens required.
a(9) corrected by Peter Gibbons, May 30 2004
A286883
Number of minimal dominating sets in the n X n queen graph.
Original entry on oeis.org
1, 4, 21, 194, 2579, 48028, 1023698, 28281838
Offset: 1
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.
Original entry on oeis.org
0, 6, 20, 12, 70, 960, 22, 352, 10, 216, 4814, 72
Offset: 1
- 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).
- 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.
Cf.
A002565 (number of ways up to isomorphism).
Showing 1-4 of 4 results.
Comments