A221537 Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

0, 3, 8, 30, 103, 364, 1276, 4483, 15740, 55274, 194095, 681576, 2393384, 8404483, 29512736, 103635366, 363920471, 1277923892, 4487489988, 15758032643, 55335074484, 194311722642, 682334774239, 2396050726160, 8413845078800

Offset

1,2

Comments

Column 3 of A221542.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

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

Empirical g.f.: x^2*(3 - x) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - Colin Barker, Oct 18 2017

Example

Some solutions for n=6
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..3....0....3....2....0....0....2....0....0....0....0....2....0....2....0....3
..3....0....1....2....0....0....2....2....3....3....1....2....3....2....0....3
..0....3....3....2....2....3....0....2....3....0....3....0....3....0....0....0
..1....1....3....0....1....3....0....2....3....0....3....1....1....1....0....0
..1....1....0....3....1....1....3....0....3....3....0....3....1....1....0....2

Crossrefs

Sequence in context: A148885 A148886 A148887 * A148888 A151440 A213860

Adjacent sequences: A221534 A221535 A221536 * A221538 A221539 A221540

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved