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

Author

R. H. Hardin, Jan 17 2013

Keywords

• nonn

Comments

Column 3 of A221459.

Examples

			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
		

Links

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

Crossrefs

Cf. A221459.

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