A221511 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

0, 3, 7, 36, 130, 532, 2088, 8304, 32876, 130376, 516704, 2048264, 8118864, 32182256, 127565600, 505652480, 2004334368, 7944899296, 31492457536, 124831656000, 494815052864, 1961376994048, 7774621408896, 30817501320448, 122156223100160

Offset: 1

Author

R. H. Hardin, Jan 18 2013

Keywords

• nonn

Comments

Column 4 of A221515.

Examples

			Some solutions for n=6
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..3....4....3....3....4....4....2....3....2....4....3....3....3....4....4....4
..0....4....3....1....0....1....4....4....4....0....3....4....0....2....0....1
..3....0....0....3....2....2....0....0....1....4....0....2....4....2....4....4
..2....4....3....3....0....0....0....1....2....0....0....4....1....4....0....2
..4....1....0....0....4....2....3....4....0....4....3....1....4....2....2....0
		

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) +6*a(n-3) +4*a(n-4) +4*a(n-6).

Empirical g.f.: x^2*(3 + x + 4*x^2 - 2*x^3 + 2*x^4) / (1 - 2*x - 6*x^2 - 6*x^3 - 4*x^4 - 4*x^6). - Colin Barker, Oct 18 2017