|
| |
|
|
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(n-1) +a(n-2) +3*a(n-3) -a(n-4) -a(n-5) for n>6.
Equivalent empirical g.f. 2*x -2*x^2*(1+x)*(2*x^3-x^2-x-2) / ( 1-x-x^2-3*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 A348396 A104723
Adjacent sequences: A197046 A197047 A197048 * A197050 A197051 A197052
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
R. H. Hardin, Oct 09 2011
|
|
|
STATUS
|
approved
|
| |
|
|
