A221679 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

0, 2, 5, 26, 100, 418, 1692, 6932, 28288, 115604, 472188, 1929012, 7880012, 32190588, 131500508, 537189116, 2194454252, 8964498844, 36620598988, 149597691420, 611116954220, 2496455194876, 10198192807820, 41660325742812

Offset: 1

Author

R. H. Hardin, Jan 22 2013

Keywords

• nonn

Comments

Column 4 of A221683.

Examples

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

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6).

Empirical g.f.: x^2*(2 - x + 3*x^2 + 2*x^3 + 2*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6). - Colin Barker, Oct 19 2017