A221677 Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

0, 2, 5, 14, 40, 113, 320, 906, 2565, 7262, 20560, 58209, 164800, 466578, 1320965, 3739886, 10588280, 29977297, 84871040, 240284954, 680289285, 1926019518, 5452902560, 15438133441, 43708091520, 123745352482, 350345021445

Offset

1,2

Comments

Column 2 of A221683.

Links

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

Formula

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

Empirical g.f.: x^2*(2 + x) / (1 - 2*x - 2*x^2 - x^3). - 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....1....1....1....1....1....1....0....1....0....1....1....1....0....0....1
..2....1....0....0....1....0....2....2....2....1....2....1....2....2....1....0
..0....1....0....0....1....0....2....2....0....1....0....2....1....2....0....0
..1....0....2....0....2....1....2....0....0....0....0....1....2....1....1....1
..0....1....2....1....2....1....1....0....1....1....0....2....1....0....0....0

Crossrefs

Sequence in context: A296516 A111109 A081908 * A229737 A059505 A159035

Adjacent sequences: A221674 A221675 A221676 * A221678 A221679 A221680

Keyword

nonn

Author

R. H. Hardin, Jan 22 2013

Status

approved