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

1,1

Comments

Column 2 of A269467.

Links

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

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)

Example

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

Crossrefs

Cf. A269467.

Sequence in context: A269531 A064831 A153582 * A096168 A051042 A121907

Adjacent sequences: A269458 A269459 A269460 * A269462 A269463 A269464

Keyword

nonn

Author

R. H. Hardin, Feb 27 2016

Status

approved