A196012 Number of n X 3 0..4 arrays with each element equal to the number its horizontal and vertical neighbors within one of itself.

1, 1, 2, 7, 13, 16, 32, 65, 125, 211, 390, 732, 1368, 2478, 4555, 8417, 15564, 28583, 52598, 96921, 178684, 328956, 605723, 1115678, 2055336, 3785356, 6971537, 12840292, 23650713, 43560381, 80229677, 147768685, 272167135, 501285666

Offset: 1

Author

R. H. Hardin, Sep 26 2011

Keywords

• nonn

Comments

Column 3 of A196017.

Examples

			All solutions for n=4:
..2..2..0....2..2..2....0..2..2....2..3..2....2..2..2....2..3..2....2..2..2
..3..3..2....2..0..2....2..3..3....3..4..3....2..0..2....3..3..3....2..0..2
..2..0..2....3..3..3....2..0..2....3..4..3....2..3..3....2..0..2....3..3..2
..2..2..2....2..3..2....2..2..2....2..3..2....0..2..2....2..2..2....2..2..0
		

Links

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

Crossrefs

Cf. A196017.

Formula

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

Empirical g.f.: x*(1 - x)*(1 + x + x^2 + 5*x^3 + 6*x^4) / (1 - x - x^2 - 3*x^4 + x^5 + 2*x^6). - Colin Barker, May 08 2018