This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A006075 M3224 #61 Feb 16 2025 08:32:29 %S A006075 1,4,4,4,5,8,10,12,14,16,21,24,28,32,36,40,46,52,57,62,68 %N A006075 Minimal number of knights needed to cover an n X n board. %C A006075 How many knights are needed to occupy or attack every square of an n X n board? %C A006075 Also known as the domination number of the n X n knight graph. - _Eric W. Weisstein_, May 27 2016 %C A006075 Upper bounds for the terms after a(20) = 62 are as follows: 68, 75, 82, 88, 96, 102, ... (see Frank Rubin's web site). %C A006075 The value a(15) = 37 given by Jackson and Pargas is wrong. A simulated annealing-based program I wrote found several complete coverages of a 15 X 15 board with 36 knights. - John Danaher (jsd(AT)mit.edu), Oct 24 2000 %D A006075 David C. Fisher, On the N X N Knight Cover Problem, Ars Combinatoria 69 (2003), 255-274. %D A006075 M. Gardner, Mathematical Magic Show. Random House, NY, 1978, p. 194. %D A006075 Anderson H. Jackson and Roy P. Pargas, Solutions to the N x N Knights Cover Problem, J. Recreat. Math., Vol. 23(4), 1991, 255-267. %D A006075 Bernard Lemaire, Knights Covers on N X N Chessboards, J. Recreat. Math., Vol. 31-2, 2003, 87-99. %D A006075 Frank Rubin, Improved knight coverings, Ars Combinatoria 69 (2003), 185-196. %D A006075 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A006075 John Watkins, Across the Board: The Mathematics of Chessboard Problems (2004), p. 97. %H A006075 J. Danaher, <a href="/A006075/a006075.txt">Results for 15 X 15 board</a>. %H A006075 Andy Huchala, <a href="/A006075/a006075.py3.txt">Python program</a>. %H A006075 Lee Morgenstern, <a href="https://web.archive.org/web/20070102070601/http://home.earthlink.net/~morgenstern/">Knight Domination</a>. [Much material, including optimality proofs for the values given in this entry] %H A006075 Frank Rubin, Contest Center Web Site, <a href="http://www.contestcen.com/knight.htm">Knight Coverings for Large Chessboards</a>. [Much material, including many illustrations] %H A006075 Frank Rubin, <a href="/A006075/a006075a.html">Illustration of three 52-knight coverings of an 18 X 18 board</a>. (see Frank Rubin's web site, from which this is taken, for many further examples) %H A006075 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>. %H A006075 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>. %H A006075 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightsProblem.html">Knights Problem</a>. %e A006075 Illustrations for a(3) = 4, a(4) = 4, a(5) = 5 (o = empty square, X = knight): %e A006075 ooo .. oooo .. ooooo %e A006075 oXo .. oXXo .. ooXoo %e A006075 XXX .. oXXo .. oXXXo %e A006075 ...... oooo .. ooXoo %e A006075 .............. ooooo %Y A006075 A006076 gives number of inequivalent ways to cover the board using a(n) knights, A103315 gives total number. %Y A006075 Cf. A075458, A075561, A189889, A342576. %K A006075 nonn,hard,more,nice %O A006075 1,2 %A A006075 _N. J. A. Sloane_ %E A006075 Terms (or bounds) through a(26) updated by Frank Rubin (contestcen(AT)aol.com), May 22 2002 %E A006075 a(20) added from the Contest Center web site by _N. J. A. Sloane_, Mar 02 2006 %E A006075 a(21) added by _Andy Huchala_, Jun 06 2021