A269578 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by more than one.

3, 9, 27, 79, 229, 659, 1889, 5401, 15419, 43977, 125355, 357191, 1017565, 2898435, 8255201, 23510865, 66956883, 190683433, 543031707, 1546443295, 4403932917, 12541401683, 35714999425, 101707905961, 289639951179, 824825396777

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(3 - 3*x - 3*x^2 + x^3) / (1 - 4*x + 2*x^2 + 4*x^3 - x^4). - Colin Barker, Jan 24 2019

Example

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

Crossrefs

Column 2 of A269583.

Sequence in context: A291020 A282087 A238440 * A026289 A027129 A077844

Adjacent sequences: A269575 A269576 A269577 * A269579 A269580 A269581

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved