A221538 Number of 0..4 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

0, 4, 14, 68, 303, 1386, 6311, 28762, 131012, 596784, 2718469, 12383368, 56409683, 256961576, 1170529586, 5332078812, 24289062227, 110643256974, 504010005519, 2295902089838, 10458455859448, 47641099074536, 217018109737881

Offset

1,2

Comments

Column 4 of A221542.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5) for n>6.

Empirical g.f.: x^2*(4 - 6*x + 10*x^2 + x^3 + x^4) / (1 - 5*x + 3*x^2 - x^3 - 15*x^4 - 3*x^5). - 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
..4....3....4....3....2....4....4....2....3....4....3....2....4....4....4....0
..3....3....0....4....4....3....0....1....3....0....2....2....0....0....0....2
..3....1....2....4....4....0....3....1....2....1....2....0....3....1....0....4
..0....4....2....3....1....4....3....1....2....3....4....0....3....4....4....4
..3....2....2....3....3....1....3....4....2....1....0....3....1....2....2....0

Crossrefs

Sequence in context: A292725 A292713 A007025 * A301511 A014512 A274804

Adjacent sequences: A221535 A221536 A221537 * A221539 A221540 A221541

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved