%I #8 Nov 02 2018 12:26:53

%S 3,5,10,25,77,279,1134,4979,22981,109453,531458,2610933,12917685,

%T 64181627,319695982,1594859887,7963472189,39784944801,198827606706,

%U 993846943841,4968361974493,24839192686975,124188113975630

%N Number of length n+2 0..6 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..6 introduced in 0..6 order.

%H R. H. Hardin, <a href="/A243515/b243515.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 52*a(n-2) + 102*a(n-3) - 91*a(n-4) + 30*a(n-5).

%F Conjectures from _Colin Barker_, Nov 02 2018: (Start)

%F G.f.: x*(3 - 31*x + 106*x^2 - 141*x^3 + 60*x^4) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 5*x)).

%F a(n) = (147 + 2^(5+n) + 4*3^(1+n) + 5^n + 36*n) / 96.

%F (End)

%e All solutions for n=3:

%e ..0....0....0....0....0....0....0....0....0....0

%e ..1....0....1....0....1....1....0....1....0....0

%e ..2....1....2....0....2....2....0....2....1....0

%e ..3....2....3....1....0....3....0....0....2....0

%e ..1....0....0....2....3....4....1....1....3....0

%Y Column 6 of A243519.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 05 2014