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

1,2

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

Links

Table of n, a(n) for n=1..13.

Eric Weisstein's World of Mathematics, Grid Graph

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

Example

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

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 *)

Crossrefs

Diagonal of A197054.

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

Sequence in context: A099553 A119694 A286760 * A175613 A296001 A121949

Adjacent sequences: A197045 A197046 A197047 * A197049 A197050 A197051

Keyword

nonn

Author

R. H. Hardin, Oct 09 2011

Status

approved