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A369692 Connected domination number of the n X n grid graph.

%I A369692 #35 Mar 21 2025 07:00:48
%S A369692 1,2,3,7,11,14,20,26,30,39,47,52,64,74,80,95
%N A369692 Connected domination number of the n X n grid graph.
%H A369692 Alexander D. Healy, <a href="/A369692/a369692.pdf">Examples of (near-)optimal dominating sets for n <= 12</a>
%H A369692 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominationNumber.html">Connected Domination Number</a>.
%H A369692 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%F A369692 a(3*n) <= n*(3*n+1); a(3*n-1) <= 3*n^2 - 1; a(3*n-2) <= (n-1)*(3*n+1). Conjecturally these inequalities hold with equality for n > 1. - _Andrew Howroyd_, Mar 06 2024
%e A369692 From _Andrew Howroyd_, Mar 06 2024: (Start)
%e A369692 a(16) = 95 = 16 + 5*14 + 4*2 + 1.
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%e A369692 (End)
%Y A369692 Cf. A104519, A287690, A302488, A370428.
%Y A369692 Cf. A381730 (numbers of minimum connected dominating sets).
%K A369692 nonn,more
%O A369692 1,2
%A A369692 _Alexander D. Healy_, Feb 25 2024
%E A369692 a(10)-a(16) from _Andrew Howroyd_, Feb 25 2024