A269462 Number of length-n 0..3 arrays with no repeated value equal to the previous repeated value.

4, 16, 60, 228, 852, 3180, 11796, 43644, 160980, 592572, 2177268, 7988700, 29277204, 107195196, 392179380, 1433907228, 5240022612, 19140884220, 69894090996, 255150047964, 931214323860, 3397977981372, 12397189043508, 45224087388060

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 18*a(n-3).

Conjectures from Colin Barker, Jan 22 2019: (Start)

G.f.: 4*x*(1 - x - 5*x^2) / ((1 - 3*x)*(1 - 2*x - 6*x^2)).

a(n) = (-28*3^n + (49-17*sqrt(7))*(1-sqrt(7))^n + (1+sqrt(7))^n*(49+17*sqrt(7))) / 63.

(End)

Example

Some solutions for n=9:
..1. .1. .2. .2. .0. .0. .1. .2. .1. .2. .0. .2. .1. .1. .1. .0
..0. .1. .1. .1. .3. .2. .3. .0. .2. .1. .1. .1. .3. .2. .2. .1
..1. .2. .2. .3. .1. .0. .2. .0. .1. .0. .3. .2. .3. .0. .2. .0
..0. .1. .3. .0. .3. .0. .1. .2. .0. .0. .0. .1. .0. .3. .1. .1
..1. .2. .0. .1. .1. .1. .0. .2. .3. .1. .2. .1. .3. .3. .1. .0
..2. .3. .3. .2. .3. .2. .1. .0. .1. .3. .1. .3. .2. .1. .0. .0
..0. .0. .0. .2. .1. .3. .2. .0. .3. .2. .1. .1. .3. .3. .3. .1
..2. .0. .1. .0. .3. .0. .0. .2. .3. .0. .2. .0. .1. .2. .0. .1
..2. .3. .0. .0. .2. .2. .3. .2. .2. .2. .2. .0. .0. .2. .0. .0

Crossrefs

Column 3 of A269467.

Sequence in context: A072335 A081161 A032106 * A047097 A051043 A123620

Adjacent sequences: A269459 A269460 A269461 * A269463 A269464 A269465

Keyword

nonn

Author

R. H. Hardin, Feb 27 2016

Status

approved