A196961 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,1,2,0,3 for x=0,1,2,3,4.

2, 6, 15, 48, 145, 449, 1397, 4342, 13500, 41981, 130562, 406025, 1262695, 3926857, 12212128, 37978464, 118109177, 367307576, 1142289291, 3552403843, 11047615721, 34356964532, 106846675430, 332282325069, 1033364333556, 3213658281627

Offset

1,1

Comments

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

Column 2 of A196967.

Links

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

Formula

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

Empirical g.f.: x*(2 + 2*x - 3*x^2 - 4*x^3 - 8*x^4 - 5*x^5 + 4*x^6) / ((1 - x)*(1 - x - 4*x^2 - 6*x^3 - 6*x^4 - x^5 + 2*x^6)). - Colin Barker, May 10 2018

Example

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

Crossrefs

Cf. A196967.

Sequence in context: A237262 A291848 A363207 * A368411 A255540 A323926

Adjacent sequences: A196958 A196959 A196960 * A196962 A196963 A196964

Keyword

nonn

Author

R. H. Hardin, Oct 08 2011

Status

approved