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A197048
Number of n X n 0..4 arrays with each element equal to the number of its horizontal and vertical zero neighbors.
3
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 09 2011
STATUS
approved