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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.
(Formerly M0884)
6

%I M0884 #42 Dec 17 2021 11:29:32

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

%N 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.

%D David C. Fisher, On the N X N Knight Cover Problem, Ars Combinatoria 69 (2003), 255-274.

%D M. Gardner, Mathematical Magic Show. Random House, NY, 1978, p. 194.

%D Bernard Lemaire, Knights Covers on N X N Chessboards, J. Recreational Mathematics, Vol. 31-2, 2003, 87-99.

%D Frank Rubin, Improved knight coverings, Ars Combinatoria 69 (2003), 185-196.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Lee Morgenstern, <a href="https://web.archive.org/web/20070102070601/http://home.earthlink.net/~morgenstern/">Knight Domination</a>.

%H Frank Rubin, <a href="http://www.contestcen.com/knight.htm">Knight coverings for large chessboards</a>, 2000.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KnightsProblem.html">Knights Problem</a>.

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

%K nonn,hard,nice

%O 1,3

%A _N. J. A. Sloane_

%E a(11) was found in 1973 by Bernard Lemaire. (_Philippe Deléham_, Jan 06 2004)

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

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