A221519 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 2 or more.

0, 6, 10, 36, 94, 274, 768, 2182, 6170, 17476, 49470, 140066, 396544, 1122694, 3178538, 8999012, 25477790, 72132146, 204218880, 578179846, 1636929594, 4634437764, 13120914558, 37147634242, 105171535360, 297759253766

Offset

1,2

Comments

Column 3 of A221524.

Links

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

Formula

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

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

Example

Some solutions for n=6
..0....2....0....2....3....0....0....3....3....2....0....1....3....1....3....1
..3....0....3....0....0....2....3....1....0....0....2....3....0....3....1....3
..0....0....0....2....1....1....1....3....0....2....3....2....1....0....1....2
..1....3....3....3....3....3....3....2....2....0....0....0....3....1....3....0
..3....3....2....0....3....2....3....0....3....2....0....3....0....3....0....3
..1....1....0....3....0....0....1....3....1....0....3....1....3....1....3....0

Crossrefs

Sequence in context: A025629 A068889 A203485 * A332984 A038264 A094890

Adjacent sequences: A221516 A221517 A221518 * A221520 A221521 A221522

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved