A221456 Number of 0..5 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..5 order.

0, 1, 2, 7, 25, 102, 455, 2192, 11203, 59814, 329343, 1851911, 10560334, 60776590, 351887190, 2045329031, 11918417465, 69563676328, 406447507101, 2376416054328, 13900548090293, 81332697848104, 475968841105687, 2785759950405621

Offset

1,3

Comments

Column 5 of A221459.

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 30*a(n-2) - 21*a(n-3) + 112*a(n-4) + 63*a(n-5) - 119*a(n-6) - 120*a(n-7) - 30*a(n-8).

Empirical g.f.: x^2*(1 - 9*x + 15*x^2 + 29*x^3 - 33*x^4 - 57*x^5 - 19*x^6) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 5*x - 5*x^2)). - Colin Barker, Aug 05 2018

Example

Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1
..2....2....0....2....2....1....2....2....0....1....1....2....2....2....0....2
..2....1....0....2....0....0....1....1....2....0....2....2....0....3....2....3
..3....3....2....0....3....0....0....1....1....2....3....1....0....4....0....3
..2....4....3....3....0....2....1....2....0....1....1....3....1....0....2....4

Crossrefs

Cf. A221459.

Sequence in context: A150510 A150511 A036784 * A221457 A221458 A221453

Adjacent sequences: A221453 A221454 A221455 * A221457 A221458 A221459

Keyword

nonn

Author

R. H. Hardin, Jan 17 2013

Status

approved