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

1,3

Comments

Column 3 of A196017.

Links

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

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

Example

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

Crossrefs

Cf. A196017.

Sequence in context: A063222 A030592 A154313 * A065104 A138645 A191060

Adjacent sequences: A196009 A196010 A196011 * A196013 A196014 A196015

Keyword

nonn

Author

R. H. Hardin, Sep 26 2011

Status

approved