A196690 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,3,0,4 for x=0,1,2,3,4.

2, 5, 11, 34, 101, 299, 890, 2643, 7855, 23340, 69355, 206087, 612384, 1819689, 5407175, 16067330, 47743801, 141869903, 421564034, 1252670447, 3722289195, 11060719828, 32866743207, 97662975451, 290203891328, 862335989181

Offset

1,1

Comments

Every 0 is next to 0 2's, every 1 is next to 1 1's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 4's.

Column 2 of A196696.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - a(n-4) for n>5.

Empirical g.f.: x*(2 + x - 5*x^2 - 3*x^3 + 2*x^4) / (1 - 2*x - 3*x^2 + x^4). - Colin Barker, Feb 22 2018

Example

Some solutions for n=4:
..0..0....0..0....0..0....0..1....1..1....0..0....0..0....1..1....1..1....0..0
..0..3....1..1....0..3....0..1....0..0....0..0....3..0....0..0....0..0....0..0
..0..0....0..0....3..0....0..0....0..0....0..3....0..0....0..1....3..0....1..0
..1..1....0..0....0..0....1..1....1..1....0..0....0..0....0..1....0..0....1..0

Crossrefs

Cf. A196696.

Sequence in context: A226919 A307316 A298122 * A101834 A117758 A284251

Adjacent sequences: A196687 A196688 A196689 * A196691 A196692 A196693

Keyword

nonn

Author

R. H. Hardin, Oct 05 2011

Status

approved