A221454 Number of 0..3 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..3 order.

0, 1, 2, 7, 24, 88, 328, 1235, 4668, 17675, 66974, 253858, 962352, 3648397, 13831870, 52440191, 198815196, 753764564, 2857736696, 10834499599, 41076702120, 155733594211, 590430871282, 2238493367822, 8486772670944, 32175798041273

Offset

1,3

Comments

Column 3 of A221459.

Links

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

Formula

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

Empirical g.f.: x^2*(1 - 2*x - 2*x^2) / ((1 - x - x^2)*(1 - 3*x - 3*x^2)). - Colin Barker, Mar 14 2018

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....1....1....1....1....1....1....1....1....1
..1....2....2....1....0....2....2....2....1....2....2....2....2....2....2....2
..0....2....3....2....1....0....1....3....2....1....1....1....3....2....3....0
..0....1....2....2....2....1....3....3....1....2....2....0....3....0....1....0
..1....3....1....0....0....3....1....2....2....3....0....3....1....3....2....1

Crossrefs

Cf. A221459.

Sequence in context: A227824 A270490 A104625 * A151293 A122446 A150390

Adjacent sequences: A221451 A221452 A221453 * A221455 A221456 A221457

Keyword

nonn

Author

R. H. Hardin, Jan 17 2013

Status

approved