%I #31 Mar 06 2024 21:48:05
%S 1,2,3,7,11,14,20,26,30,39,47,52,64,74,80,95
%N Connected domination number of the n X n grid graph.
%H Alexander D. Healy, <a href="/A369692/a369692.pdf">Examples of (near-)optimal dominating sets for n <= 12</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/GridGraph.html">Grid Graph</a>.
%F 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 From _Andrew Howroyd_, Mar 06 2024: (Start)
%e a(16) = 95 = 16 + 5*14 + 4*2 + 1.
%e . . . . . . . . . . . . . . . .
%e X X X X X X X X X X X X X X X X
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X X X
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X X X
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X X X
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X X X
%e . X . . X . . X . . X . . X . .
%e . X . . X . . X . . X . . X X .
%e (End)
%Y Cf. A104519, A287690, A302488, A370428.
%K nonn,more
%O 1,2
%A _Alexander D. Healy_, Feb 25 2024
%E a(10)-a(16) from _Andrew Howroyd_, Feb 25 2024