A197444 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,1,0,0 for x=0,1,2,3,4.

2, 5, 12, 36, 107, 321, 957, 2868, 8581, 25694, 76914, 230273, 689377, 2063867, 6178778, 18498023, 55379290, 165794354, 496354537, 1485984549, 4448735449, 13318609060, 39873206463, 119372269782, 357376295102, 1069911935955

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

Column 2 of A197450.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -6*a(n-4) -a(n-5) +4*a(n-7) +a(n-8).

Empirical g.f.: x*(2 + x - 8*x^2 - 5*x^3 + 7*x^4 + 7*x^5 + x^6 - 3*x^7) / ((1 - x)*(1 - x - 6*x^2 - 2*x^3 + 4*x^4 + 5*x^5 + 5*x^6 + x^7)). - Colin Barker, May 12 2018

Example

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

Crossrefs

Cf. A197450.

Sequence in context: A303204 A333411 A032203 * A094717 A323933 A038142

Adjacent sequences: A197441 A197442 A197443 * A197445 A197446 A197447

Keyword

nonn

Author

R. H. Hardin, Oct 15 2011

Status

approved