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

Author

R. H. Hardin, Jan 19 2013

Keywords

• nonn

Comments

Column 3 of A221542.

Examples

			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
		

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