A381730 Number of minimum connected dominating sets in the n X n grid graph.

1, 4, 2, 16, 126, 24, 800, 16288, 16, 87216, 3554000, 16, 13400336, 882342944, 16, 2376303680

Offset: 1

Author

Eric W. Weisstein, Mar 05 2025

Keywords

• nonn
• more

Examples

			From _Andrew Howroyd_, Mar 19 2025: (Start)
One of 16 arrangements for a(9):
  . 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

• Eric Weisstein's World of Mathematics, Connected Dominating Set.
• Eric Weisstein's World of Mathematics, Grid Graph.
• Eric W. Weisstein, Symmetrically inequivalent minimum configurations with multiplicities for n = 1 to 6 plus 9, 12, 15, 18
• Eric W. Weisstein, Symmetrically inequivalent minimum configurations with multiplicities for n = 7

Crossrefs

Main diagonal of A381474.

Cf. A287690, A347632.

Cf. A369692 (connected domination numbers).

Formula

a(3*n) = 16 for n >= 3. - Andrew Howroyd, Mar 19 2025

Extensions

a(6)-a(16) from Andrew Howroyd, Mar 19 2025