A221512 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

0, 4, 13, 80, 381, 1970, 9940, 50495, 255980, 1298632, 6586395, 33407907, 169448914, 859472004, 4359369001, 22111382192, 112152257687, 568853184739, 2885309153794, 14634723355722, 74229524701062, 376503348140640

Offset

1,2

Comments

Column 5 of A221515.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +11*a(n-2) +20*a(n-3) +17*a(n-4) -3*a(n-5) +a(n-6).

Empirical g.f.: x^2*(4 + 5*x + 10*x^2 - 2*x^3) / (1 - 2*x - 11*x^2 - 20*x^3 - 17*x^4 + 3*x^5 - 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
..2....2....4....5....2....3....3....4....3....5....2....3....3....3....2....5
..3....5....0....3....3....0....1....0....0....2....3....5....0....5....0....2
..1....1....0....1....1....5....3....2....5....2....5....0....2....0....0....0
..2....1....4....2....1....0....5....1....4....4....2....3....1....5....4....3
..4....3....1....4....4....2....2....3....2....0....5....1....4....1....0....5

Crossrefs

Sequence in context: A337286 A140417 A301396 * A061143 A354152 A354409

Adjacent sequences: A221509 A221510 A221511 * A221513 A221514 A221515

Keyword

nonn

Author

R. H. Hardin, Jan 18 2013

Status

approved