A196858 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,4,2,0,1 for x=0,1,2,3,4.

1, 3, 7, 12, 26, 56, 113, 235, 490, 1012, 2099, 4356, 9026, 18714, 38806, 80450, 166797, 345830, 717003, 1486565, 3082117, 6390162, 13248759, 27468753, 56951126, 118077121, 244810064, 507566235, 1052340264, 2181823742, 4523588913

Offset

1,2

Comments

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

Column 3 of A196863.

Links

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

Formula

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

Empirical g.f.: x*(1 + x + 2*x^2 - 2*x^3 + 2*x^4 - x^5) / (1 - 2*x + x^2 - 3*x^3 + 2*x^4 - 2*x^5 + x^6). - Colin Barker, May 09 2018

Example

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

Crossrefs

Cf. A196863.

Sequence in context: A280345 A062325 A301982 * A099811 A196917 A256259

Adjacent sequences: A196855 A196856 A196857 * A196859 A196860 A196861

Keyword

nonn

Author

R. H. Hardin, Oct 06 2011

Status

approved