A221520 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 2 or more.

0, 12, 30, 144, 536, 2172, 8544, 33960, 134480, 533248, 2113456, 8377808, 33207936, 131632288, 521770784, 2068227136, 8198158272, 32496344448, 128810916224, 510588286464, 2023899853184, 8022453208832, 31799871553536, 126050200002816

Offset

1,2

Comments

Column 4 of A221524.

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.: 2*x^2*(6 + 3*x + 6*x^2 - 2*x^3 + 4*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....1....4....3....3....0....0....3....3....3....3....0....1....0....4....1
..2....4....1....0....0....2....4....1....1....0....0....2....4....3....1....3
..0....1....2....0....0....1....2....1....0....2....4....2....2....3....3....4
..0....0....4....4....4....4....3....3....3....4....2....0....0....0....1....2
..2....4....2....3....4....0....0....0....3....1....2....1....3....0....0....4
..0....1....0....0....1....3....4....4....1....3....4....3....1....2....3....0

Crossrefs

Cf. A221524.

Sequence in context: A260417 A117313 A080563 * A214311 A005147 A320122

Adjacent sequences: A221517 A221518 A221519 * A221521 A221522 A221523

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved