A269771 Number of length-n 0..3 arrays with every repeated value unequal to the previous repeated value plus one mod 3+1.

4, 16, 64, 252, 984, 3816, 14724, 56592, 216864, 829116, 3164184, 12058632, 45904644, 174598416, 663634944, 2521077372, 9573268824, 36340434216, 137913296004, 523277751312, 1985122823904, 7529850771516, 28558867923864

Offset

1,1

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 9*a(n-3).

Empirical g.f.: 4*x*(1 - 2*x - 2*x^2) / ((1 - 3*x)*(1 - 3*x - 3*x^2)). - Colin Barker, Jan 28 2019

Example

Some solutions for n=8:
..1. .3. .2. .3. .3. .1. .2. .0. .2. .0. .3. .3. .3. .2. .3. .1
..0. .0. .1. .1. .2. .3. .0. .2. .3. .3. .3. .3. .0. .1. .0. .0
..1. .0. .3. .1. .3. .0. .3. .2. .0. .2. .0. .1. .1. .2. .1. .0
..2. .3. .3. .1. .3. .2. .1. .2. .2. .2. .1. .0. .0. .0. .0. .1
..3. .3. .3. .1. .1. .1. .2. .2. .0. .1. .1. .1. .3. .0. .1. .0
..1. .1. .1. .1. .1. .1. .3. .3. .2. .0. .0. .2. .0. .1. .1. .0
..3. .0. .0. .1. .3. .1. .0. .0. .2. .0. .3. .0. .0. .2. .1. .0
..0. .1. .2. .2. .2. .0. .3. .3. .3. .3. .2. .1. .0. .2. .2. .1

Crossrefs

Column 3 of A269776.

Sequence in context: A259898 A307945 A370143 * A228980 A188714 A005755

Adjacent sequences: A269768 A269769 A269770 * A269772 A269773 A269774

Keyword

nonn

Author

R. H. Hardin, Mar 04 2016

Status

approved