A221511 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

0, 3, 7, 36, 130, 532, 2088, 8304, 32876, 130376, 516704, 2048264, 8118864, 32182256, 127565600, 505652480, 2004334368, 7944899296, 31492457536, 124831656000, 494815052864, 1961376994048, 7774621408896, 30817501320448, 122156223100160

Offset

1,2

Comments

Column 4 of A221515.

Links

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

Formula

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

Empirical g.f.: x^2*(3 + x + 4*x^2 - 2*x^3 + 2*x^4) / (1 - 2*x - 6*x^2 - 6*x^3 - 4*x^4 - 4*x^6). - 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
..3....4....3....3....4....4....2....3....2....4....3....3....3....4....4....4
..0....4....3....1....0....1....4....4....4....0....3....4....0....2....0....1
..3....0....0....3....2....2....0....0....1....4....0....2....4....2....4....4
..2....4....3....3....0....0....0....1....2....0....0....4....1....4....0....2
..4....1....0....0....4....2....3....4....0....4....3....1....4....2....2....0

Crossrefs

Sequence in context: A063042 A108505 A047158 * A102917 A156465 A049366

Adjacent sequences: A221508 A221509 A221510 * A221512 A221513 A221514

Keyword

nonn

Author

R. H. Hardin, Jan 18 2013

Status

approved