A218419 Number of n X n binary arrays with every 0 a horizontal, vertical or antidiagonal neighbor to some 1.

1, 13, 357, 41515, 19003811, 34328798853, 245489633250861, 6942897327251230265, 776657742366634012014603, 343639983448734808976866431015, 601395784904377113605427806277106571, 4162939904811020936134310707612968666170209

Offset

1,2

Comments

Number of dominating sets in the graph which is an n X n rhombus in the hexagonal lattice. - Andrew Howroyd, Jul 16 2026

Links

R. H. Hardin, Table of n, a(n) for n = 1..12

Eric Weisstein's World of Mathematics, Dominating Set.

Example

Some solutions for n=3:
..1..1..1....1..1..0....1..1..1....0..0..0....0..1..1....1..1..0....0..1..0
..0..1..1....0..1..0....1..1..1....1..1..0....0..1..1....1..0..1....1..0..0
..1..0..1....0..1..1....0..1..1....1..1..0....0..0..1....0..0..0....1..1..1

Crossrefs

Main diagonal of A218426.

Sequence in context: A220636 A078738 A394524 * A165391 A061015 A330255

Adjacent sequences: A218416 A218417 A218418 * A218420 A218421 A218422

Keyword

nonn,changed

Author

R. H. Hardin, Oct 28 2012

Extensions

New name from Andrew Howroyd, Jul 16 2026

Status

approved