A221536 Number of 0..2 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

0, 2, 4, 10, 22, 54, 134, 334, 822, 2014, 4934, 12110, 29750, 73086, 179494, 440750, 1082262, 2657630, 6526342, 16026766, 39356662, 96646974, 237332966, 582812014, 1431196758, 3514554142, 8630600774, 21193942094, 52045411766, 127806567678

Offset

1,2

Comments

Column 2 of A221542.

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) +4*a(n-4).

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

Example

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

Crossrefs

Sequence in context: A164990 A348009 A121285 * A290277 A030234 A205490

Adjacent sequences: A221533 A221534 A221535 * A221537 A221538 A221539

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved