%I
%S 3,5,10,24,65,187,552,1646,4927,14769,44294,132868,398589,1195751,
%T 3587236,10761690,32285051,96855133,290565378,871696112,2615088313,
%U 7845264915,23535794720,70607384134,211822152375,635466457097
%N Number of length n+2 0..4 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..4 introduced in 0..4 order.
%H R. H. Hardin, <a href="/A243513/b243513.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n1)  7*a(n2) + 3*a(n3).
%F Conjectures from _Colin Barker_, Nov 02 2018: (Start)
%F G.f.: x*(3  10*x + 6*x^2) / ((1  x)^2*(1  3*x)).
%F a(n) = (7 + 3^n + 2*n) / 4.
%F (End)
%e All solutions for n=3:
%e ..0....0....0....0....0....0....0....0....0....0
%e ..1....0....1....0....0....1....1....1....0....0
%e ..2....0....2....1....0....2....2....2....0....1
%e ..3....1....0....2....0....0....3....3....0....2
%e ..0....2....1....3....1....3....1....4....0....0
%Y Column 4 of A243519.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jun 05 2014
