A221510 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

0, 2, 3, 12, 30, 89, 248, 706, 1995, 5652, 15998, 45297, 128240, 363074, 1027923, 2910236, 8239390, 23327177, 66043368, 186980482, 529374875, 1498754084, 4243238398, 12013359841, 34011950560, 96293859202, 272624979363

Offset: 1

Author

R. H. Hardin, Jan 18 2013

Keywords

• nonn

Comments

Column 3 of A221515.

Examples

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

Links

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

Formula

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

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