A221678 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

0, 2, 5, 20, 68, 241, 844, 2966, 10413, 36568, 128408, 450913, 1583400, 5560186, 19524853, 68562444, 240760252, 845440977, 2968805844, 10425101678, 36608235997, 128551546480, 451414815600, 1585164405441, 5566379537040

Offset: 1

Author

R. H. Hardin, Jan 22 2013

Keywords

• nonn

Comments

Column 3 of A221683.

Examples

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

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*(2 - x + x^2) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - Colin Barker, Oct 19 2017