A103315 - OEIS

%I #39 Feb 16 2025 08:32:56

%S 1,1,8,9,47,127,10,2,2,4,800,2,152,4,504,2,212,19562

%N Number of minimum dominating sets for the n X n knight graph.

%C In other words, as made explicit in the old name: Sequence A006075 gives minimum number of knights needed to cover an n X n board (i.e., the domination number of the n X n knight graph).  This sequence (A103315) gives total number of solutions using A006075(n) knights (compare A006076).

%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="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>

%Y Cf. A006075 (domination number of the n X n knight graph).

%Y Cf. A006076 (inequivalent number of minimum dominating sets).

%Y Cf. A098604.

%K nonn,more

%O 1,3

%A _N. J. A. Sloane_, Mar 20 2005, following a suggestion from Lee Morgenstern.

%E New name from _Eric W. Weisstein_, Sep 06 2021