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

1, 2, 3, 7, 11, 14, 20, 26, 30, 39, 47, 52, 64, 74, 80, 95

Offset: 1

Author

Alexander D. Healy, Feb 25 2024

Keywords

• nonn
• more

Examples

			From _Andrew Howroyd_, Mar 06 2024: (Start)
a(16) = 95 = 16 + 5*14 + 4*2 + 1.
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  X X X X X X X X X X X X X X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X X
  . X . . X . . X . . X . . X . .
  . X . . X . . X . . X . . X X .
(End)
		

Links

• Alexander D. Healy, Examples of (near-)optimal dominating sets for n <= 12
• Eric Weisstein's World of Mathematics, Connected Domination Number.
• Eric Weisstein's World of Mathematics, Grid Graph.

Crossrefs

Cf. A104519, A287690, A302488, A370428.

Cf. A381730 (numbers of minimum connected dominating sets).

Formula

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

Extensions

a(10)-a(16) from Andrew Howroyd, Feb 25 2024