A196917 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,4,0 for x=0,1,2,3,4.

1, 3, 7, 12, 27, 58, 121, 257, 545, 1153, 2442, 5172, 10952, 23193, 49116, 104012, 220265, 466453, 987802, 2091857, 4429902, 9381153, 19866361, 42070767, 89092785, 188670778, 399545962, 846113942, 1791805877, 3794486938, 8035541856

Offset

1,2

Comments

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

Column 3 of A196922.

Links

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

Formula

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

Empirical g.f.: x*(1 + x + x^2 - 3*x^3 + x^4) / (1 - 2*x - x^3 + x^4). - Colin Barker, May 09 2018

Example

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

Crossrefs

Cf. A196922.

Sequence in context: A301982 A196858 A099811 * A256259 A182941 A063072

Adjacent sequences: A196914 A196915 A196916 * A196918 A196919 A196920

Keyword

nonn

Author

R. H. Hardin, Oct 07 2011

Status

approved