login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A197049 Number of n X 3 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors. 5
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: A189892 A240877 A218008 * A104723 A206140 A079162

Adjacent sequences:  A197046 A197047 A197048 * A197050 A197051 A197052

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 09 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 26 10:31 EDT 2017. Contains 292518 sequences.