A197229 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,0,1,2 for x=0,1,2,3,4.

1, 7, 12, 31, 79, 186, 465, 1131, 2776, 6803, 16663, 40842, 100065, 245207, 600844, 1472287, 3607663, 8840098, 21661545, 53078827, 130062864, 318702387, 780939327, 1913591746, 4689011265, 11489821079, 28154333788, 68988586095, 169047687279

Offset

1,2

Comments

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

Column 2 of A197235.

Links

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

Formula

Empirical: a(n) = a(n-1) +3*a(n-2) +2*a(n-3) -a(n-4) -a(n-5) -a(n-6).

Empirical g.f.: x*(1 + 6*x + 2*x^2 - 4*x^3 - x^4 - 2*x^5) / (1 - x - 3*x^2 - 2*x^3 + x^4 + x^5 + x^6). - Colin Barker, Feb 18 2018

Example

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

Crossrefs

Sequence in context: A078575 A220036 A330589 * A316088 A198306 A218554

Adjacent sequences: A197226 A197227 A197228 * A197230 A197231 A197232

Keyword

nonn

Author

R. H. Hardin, Oct 12 2011

Status

approved