A006076 Sequence A006075 gives minimal number of knights needed to cover an n X n board. This sequence gives number of inequivalent solutions using A006075(n) knights.

1, 1, 2, 3, 8, 23, 3, 1, 1, 2, 100, 1, 20, 1, 63, 1, 29, 2551

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice

References

• David C. Fisher, On the N X N Knight Cover Problem, Ars Combinatoria 69 (2003), 255-274.
• M. Gardner, Mathematical Magic Show. Random House, NY, 1978, p. 194.
• Bernard Lemaire, Knights Covers on N X N Chessboards, J. Recreational Mathematics, Vol. 31-2, 2003, 87-99.
• Frank Rubin, Improved knight coverings, Ars Combinatoria 69 (2003), 185-196.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Lee Morgenstern, Knight Domination.
• Frank Rubin, Knight coverings for large chessboards, 2000.
• Eric Weisstein's World of Mathematics, Knights Problem.

Crossrefs

Cf. A006075 (number of solutions), A098604 (rectangular board). A103315 gives the total number of solutions.

Extensions

a(11) was found in 1973 by Bernard Lemaire. (Philippe Deléham, Jan 06 2004)

a(13)-a(17) from the Morgenstern web site, Nov 08 2004

a(18) from the Morgenstern web site, Mar 20 2005