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

1,2

Comments

Column 4 of A221683.

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

Example

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

Crossrefs

Sequence in context: A204275 A160048 A019047 * A178390 A045903 A090878

Adjacent sequences: A221676 A221677 A221678 * A221680 A221681 A221682

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved