A221567 Number of 0..2 arrays of length n with each element differing from at least one neighbor by something other than 1

0, 5, 9, 25, 57, 141, 345, 853, 2097, 5149, 12633, 31013, 76161, 187053, 459369, 1128053, 2770065, 6802301, 16704249, 41020357, 100732833, 247366989, 607452297, 1491704341, 3663139761, 8995478557, 22089965337, 54245756261, 133209897153

Offset

1,2

Comments

Column 2 of A221573

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.: -x^2*(5-6*x+8*x^2) / ( -1+3*x-2*x^2+4*x^4 ). - R. J. Mathar, Jun 06 2013

Example

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

Crossrefs

Sequence in context: A127976 A147286 A137199 * A147512 A301960 A050359

Adjacent sequences: A221564 A221565 A221566 * A221568 A221569 A221570

Keyword

nonn

Author

R. H. Hardin Jan 20 2013

Status

approved