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

Author

R. H. Hardin, Mar 01 2016

Keywords

• nonn

Comments

Column 2 of A269619.

Examples

			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
		

Links

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

Crossrefs

Cf. A269619.

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)