

A197049


Number of n X 3 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.


6



2, 4, 10, 18, 38, 78, 156, 320, 654, 1326, 2706, 5518, 11228, 22884, 46634, 94978, 193518, 394286, 803220, 1636448, 3334030, 6792334, 13838202, 28192958, 57437684, 117018884, 238404906, 485705682, 989536598, 2016000430, 4107230284
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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.
In other words, the number of maximal independent vertex sets (and minimal vertex covers) in the 3 X n grid graph.  Eric W. Weisstein, Aug 07 2017


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set
Eric Weisstein's World of Mathematics, Minimal Vertex Cover


FORMULA

Empirical: a(n) = a(n1) +a(n2) +3*a(n3) a(n4) a(n5) for n>6.
Equivalent empirical g.f. 2*x 2*x^2*(1+x)*(2*x^3x^2x2) / ( 1xx^23*x^3+x^4+x^5 ).  R. J. Mathar, Oct 10 2011


EXAMPLE

Some solutions for n=5
..2..0..2....0..1..1....2..0..1....0..3..0....0..3..0....0..3..0....0..2..0
..0..4..0....1..2..0....0..2..1....3..0..2....2..0..2....2..0..3....1..1..1
..2..0..3....2..0..3....2..1..0....0..2..1....1..1..1....1..2..0....1..0..2
..1..2..0....0..4..0....0..2..1....1..2..0....0..3..0....0..2..1....1..2..0
..0..1..1....2..0..2....2..0..1....1..0..2....2..0..2....2..0..1....0..1..1


CROSSREFS

Column 3 of A197054.
Sequence in context: A240877 A218008 A303346 * A303438 A104723 A206140
Adjacent sequences: A197046 A197047 A197048 * A197050 A197051 A197052


KEYWORD

nonn


AUTHOR

R. H. Hardin, Oct 09 2011


STATUS

approved



