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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 16 2016
STATUS
approved