%I #8 Nov 03 2018 08:39:39
%S 3,6,12,25,53,115,253,564,1268,2871,6531,14911,34127,78250,179644,
%T 412797,949145,2183355,5024025,11563144,26617508,61278283,141084439,
%U 324844263,747976187,1722312558,3965923308,9132346753,21029284637,48424978627
%N Number of length n+2 0..3 arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..3 introduced in 0..3 order.
%H R. H. Hardin, <a href="/A243722/b243722.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n1) + 3*a(n2)  4*a(n3)  3*a(n4).
%F Empirical g.f.: x*(3  9*x^2  5*x^3) / ((1  x  x^2)*(1  x  3*x^2)).  _Colin Barker_, Nov 03 2018
%e Some solutions for n=6:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....0....1....1....1....1....0....1....1....1....1....1....1....1....1....0
%e ..0....1....0....0....0....1....1....1....0....1....0....1....1....0....1....1
%e ..1....0....1....0....0....0....1....0....0....2....1....2....2....1....2....0
%e ..1....1....0....1....1....1....2....0....2....2....1....2....2....1....1....0
%e ..0....0....0....1....1....1....2....2....0....0....0....1....3....2....1....1
%e ..0....0....2....2....0....0....0....0....0....2....0....1....2....1....2....1
%e ..1....2....2....2....0....1....0....2....3....0....2....2....2....2....1....0
%Y Column 3 of A243729.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 09 2014
