A269488 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by one.

3, 9, 27, 77, 215, 591, 1609, 4353, 11731, 31543, 84721, 227481, 610947, 1641823, 4415873, 11888737, 32041667, 86449895, 233495441, 631307785, 1708559779, 4628272463, 12548119617, 34047086033, 92447178723, 251183783319

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 9*a(n-2) - 4*a(n-3) + 10*a(n-4) + 4*a(n-5).

Empirical g.f.: x*(3 - 9*x + 8*x^3 + 2*x^4) / ((1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)). - Colin Barker, Jan 23 2019

Example

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

Crossrefs

Column 2 of A269494.

Sequence in context: A182897 A228734 A048481 * A027027 A361845 A140348

Adjacent sequences: A269485 A269486 A269487 * A269489 A269490 A269491

Keyword

nonn

Author

R. H. Hardin, Feb 28 2016

Status

approved