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

%I A268939 #8 Jan 16 2019 15:53:38
%S A268939 4,16,60,220,788,2780,9684,33404,114292,388444,1312788,4415548,
%T A268939 14790836,49369628,164279892,545170172,1804855540,5962578652,
%U A268939 19661140116,64722276796,212738159924,698312564636,2289419181780,7497612860540
%N A268939 Number of length-n 0..3 arrays with no repeated value unequal to the previous repeated value plus one mod 3+1.
%H A268939 R. H. Hardin, <a href="/A268939/b268939.txt">Table of n, a(n) for n = 1..210</a>
%F A268939 Empirical: a(n) = 5*a(n-1) - 2*a(n-2) - 12*a(n-3).
%F A268939 Conjectures from _Colin Barker_, Jan 16 2019: (Start)
%F A268939 G.f.: 4*x*(1 - x - 3*x^2) / ((1 - 3*x)*(1 - 2*x - 4*x^2)).
%F A268939 a(n) = (-40*3^n + (25-11*sqrt(5))*(1-sqrt(5))^n + (1+sqrt(5))^n*(25+11*sqrt(5))) / 10.
%F A268939 (End)
%e A268939 Some solutions for n=9:
%e A268939 ..3. .1. .0. .0. .2. .2. .0. .1. .2. .0. .2. .0. .2. .2. .2. .1
%e A268939 ..0. .1. .2. .2. .0. .3. .3. .3. .0. .0. .1. .1. .0. .0. .1. .3
%e A268939 ..2. .3. .3. .3. .1. .0. .2. .0. .0. .2. .3. .1. .3. .2. .3. .0
%e A268939 ..0. .1. .3. .2. .3. .1. .1. .3. .2. .3. .1. .0. .1. .0. .0. .2
%e A268939 ..2. .2. .0. .1. .1. .3. .2. .0. .3. .1. .3. .1. .3. .3. .1. .1
%e A268939 ..2. .1. .3. .1. .2. .0. .2. .3. .2. .3. .2. .0. .2. .3. .2. .3
%e A268939 ..1. .3. .0. .0. .3. .0. .0. .0. .3. .1. .3. .2. .0. .2. .1. .1
%e A268939 ..2. .2. .1. .2. .2. .1. .2. .1. .1. .2. .1. .2. .1. .3. .1. .2
%e A268939 ..0. .2. .0. .0. .0. .2. .1. .1. .3. .0. .1. .0. .3. .0. .3. .1
%Y A268939 Column 3 of A268944.
%K A268939 nonn
%O A268939 1,1
%A A268939 _R. H. Hardin_, Feb 16 2016