A268939 Number of length-n 0..3 arrays with no repeated value unequal to the previous repeated value plus one mod 3+1.

4, 16, 60, 220, 788, 2780, 9684, 33404, 114292, 388444, 1312788, 4415548, 14790836, 49369628, 164279892, 545170172, 1804855540, 5962578652, 19661140116, 64722276796, 212738159924, 698312564636, 2289419181780, 7497612860540

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 2*a(n-2) - 12*a(n-3).

Conjectures from Colin Barker, Jan 16 2019: (Start)

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

a(n) = (-40*3^n + (25-11*sqrt(5))*(1-sqrt(5))^n + (1+sqrt(5))^n*(25+11*sqrt(5))) / 10.

(End)

Example

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

Crossrefs

Column 3 of A268944.

Sequence in context: A120926 A255303 A273347 * A269635 A267928 A269532

Adjacent sequences: A268936 A268937 A268938 * A268940 A268941 A268942

Keyword

nonn

Author

R. H. Hardin, Feb 16 2016

Status

approved