A269613 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

3, 9, 27, 78, 222, 624, 1740, 4824, 13320, 36672, 100752, 276384, 757344, 2073600, 5674176, 15520128, 42437760, 116014080, 317100288, 866621952, 2368230912, 6471278592, 17682164736, 48313178112, 132003268608, 360658059264

Offset

1,1

Comments

Column 2 of A269619.

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).

Conjectures from Colin Barker, Mar 21 2018: (Start)

G.f.: 3*x*(1 - x - x^2) / ((1 - 2*x)*(1 - 2*x - 2*x^2)).

a(n) = (-3*2^n + (3-2*sqrt(3))*(1-sqrt(3))^n + (1+sqrt(3))^n*(3+2*sqrt(3))) / 4.

(End)

Example

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

Crossrefs

Cf. A269619.

Sequence in context: A370142 A241574 A268013 * A006810 A090401 A181137

Adjacent sequences: A269610 A269611 A269612 * A269614 A269615 A269616

Keyword

nonn

Author

R. H. Hardin, Mar 01 2016

Status

approved