

A197048


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


2



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


CROSSREFS

Diagonal of A197054.
Cf. A006506 (independent vertex sets), A133515 (dominating sets).
Sequence in context: A099553 A119694 A286760 * A175613 A121949 A005144
Adjacent sequences: A197045 A197046 A197047 * A197049 A197050 A197051


KEYWORD

nonn,changed


AUTHOR

R. H. Hardin, Oct 09 2011


STATUS

approved



