A269461 Number of length-n 0..2 arrays with no repeated value equal to the previous repeated value.

3, 9, 24, 66, 174, 462, 1206, 3150, 8166, 21150, 54582, 140718, 362118, 931134, 2391894, 6141006, 15757734, 40420062, 103647606, 265721070, 681097926, 1745555070, 4473092502, 11461604238, 29366557158, 75238139934, 192754700214

Offset: 1

Author

R. H. Hardin, Feb 27 2016

Keywords

• nonn

Comments

Column 2 of A269467.

Examples

			Some solutions for n=9:
..1. .1. .0. .2. .1. .0. .1. .2. .2. .1. .1. .0. .2. .2. .0. .2
..1. .2. .1. .2. .2. .1. .0. .1. .1. .0. .1. .2. .0. .1. .1. .1
..0. .2. .2. .1. .1. .2. .1. .1. .0. .0. .0. .1. .1. .1. .0. .1
..2. .0. .2. .2. .2. .2. .2. .0. .0. .1. .2. .2. .1. .0. .1. .2
..2. .1. .0. .0. .0. .1. .2. .2. .2. .2. .0. .0. .2. .0. .0. .0
..1. .0. .2. .1. .1. .0. .0. .2. .1. .2. .0. .1. .1. .2. .2. .0
..2. .1. .1. .1. .0. .2. .2. .1. .1. .0. .1. .0. .0. .2. .1. .2
..0. .1. .2. .0. .0. .1. .1. .0. .0. .2. .2. .1. .2. .1. .1. .2
..1. .0. .1. .0. .1. .0. .0. .1. .1. .1. .2. .0. .0. .1. .2. .0
		

Links

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

Crossrefs

Cf. A269467.

Formula

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

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

G.f.: 3*x*(1 - 3*x^2) / ((1 - 2*x)*(1 - x - 4*x^2)).

a(n) = 2^(-4-n)*(-51*4^(1+n) + (255-57*sqrt(17))*(1-sqrt(17))^n + 3*(1+sqrt(17))^n*(85+19*sqrt(17))) / 17.

(End)