%I #39 Mar 01 2024 08:00:26
%S 1,1,1,4,5,8,12,15,20,24,28,33,39,46,52,58
%N Connected domination number of the n X n king graph.
%C In other words, a(n) is the minimum number of kings that can be placed on an n X n chessboard such that (i) the occupied squares form a single connected component, and (ii) every square is either occupied by a king or adjacent to one that is.
%C a(17) <= 67; a(18) <= 75; a(19) <= 83; a(20) <= 92.
%H Alexander D. Healy, <a href="/A370428/a370428_4.pdf">Examples of (near-)optimal connected dominating sets for n <= 20</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedDominationNumber.html">Connected Domination Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingGraph.html">King Graph</a>.
%Y Cf. A075561, A289180, A302401, A369692.
%K nonn,more
%O 1,4
%A _Alexander D. Healy_, Feb 24 2024
%E a(13)-a(16) from _Andrew Howroyd_, Feb 25 2024