A197048 Number of n X n 0..4 arrays with each element equal to the number of its horizontal and vertical zero neighbors.

1, 2, 10, 42, 358, 4468, 88056, 2745186, 134355866, 10264692132, 1234801357470, 232966546265096, 68939282741912248

Offset: 1

Author

R. H. Hardin, Oct 09 2011

Keywords

• nonn

Comments

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's.

Also, the number of maximal independent vertex sets in the grid graph P_n X P_n. - Andrew Howroyd, May 16 2017

Examples

			Some solutions for n=4
..0..2..0..2....2..0..1..1....2..0..3..0....0..3..0..2....1..0..3..0
..1..1..2..0....0..3..1..0....0..4..0..2....3..0..3..0....1..2..0..3
..2..0..2..1....3..0..2..1....3..0..2..1....0..2..1..1....0..1..3..0
..0..3..0..1....0..3..0..1....0..2..1..0....1..1..0..1....1..1..0..2
		

Links

• Eric Weisstein's World of Mathematics, Grid Graph
• Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

Crossrefs

Diagonal of A197054.

Cf. A006506 (independent vertex sets), A133515 (dominating sets).

Programs

Mathematica

A197054 = Cases[Import["https://oeis.org/A197054/b197054.txt", "Table"], {, }][[All, 2]];
a[n_] := A197054[[2 n^2 - 2 n + 1]];
Table[a[n], {n, 1, 13}] (* Jean-François Alcover, Sep 23 2019 *)