A269601 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by one or less.

3, 9, 24, 62, 154, 376, 902, 2142, 5040, 11786, 27418, 63544, 146822, 338478, 778944, 1790282, 4110730, 9432424, 21633542, 49603134, 113717328, 260691722, 597649402, 1370287384, 3142264070, 7206988878, 16533117792, 37935980618, 87065571946

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 5*a(n-2) - 8*a(n-3) + 12*a(n-4).

Empirical g.f.: x*(3 - 6*x - 6*x^2 + 11*x^3) / ((1 - 2*x)^2*(1 - x - 3*x^2)). - Colin Barker, Jan 24 2019

Example

Some solutions for n=7:
..2. .2. .2. .2. .2. .0. .1. .0. .2. .2. .2. .1. .0. .1. .2. .2
..1. .1. .1. .1. .0. .2. .2. .2. .0. .0. .1. .2. .2. .2. .0. .1
..2. .1. .0. .2. .2. .1. .1. .2. .0. .1. .0. .2. .1. .1. .1. .0
..0. .2. .2. .1. .1. .0. .1. .1. .2. .1. .1. .0. .0. .0. .0. .1
..1. .1. .0. .0. .0. .2. .2. .0. .0. .0. .0. .1. .2. .1. .1. .2
..1. .0. .1. .2. .2. .0. .0. .2. .1. .1. .0. .2. .1. .0. .0. .1
..2. .1. .0. .0. .1. .0. .1. .0. .2. .2. .2. .0. .1. .2. .1. .0

Crossrefs

Column 2 of A269606.

Sequence in context: A117585 A317474 A279978 * A006684 A342795 A267465

Adjacent sequences: A269598 A269599 A269600 * A269602 A269603 A269604

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved