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A243514 Number of length n+2 0..5 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..5 introduced in 0..5 order.

%I A243514 #8 Nov 02 2018 12:29:32
%S A243514 3,5,10,25,76,263,978,3773,14824,58771,234046,934121,3732372,14921279,
%T A243514 59668714,238642069,954502720,3817879787,15271256982,61084503617,
%U A243514 244336965868,977345766295,3909378870850,15637507094765,62550011601816
%N A243514 Number of length n+2 0..5 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..5 introduced in 0..5 order.
%H A243514 R. H. Hardin, <a href="/A243514/b243514.txt">Table of n, a(n) for n = 1..210</a>
%F A243514 Empirical: a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4).
%F A243514 Conjectures from _Colin Barker_, Nov 02 2018: (Start)
%F A243514 G.f.: x*(3 - 19*x + 33*x^2 - 16*x^3) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)).
%F A243514 a(n) = (26 + 9*2^n + 4^n + 6*n) / 18.
%F A243514 (End)
%e A243514 All solutions for n=3:
%e A243514 ..0....0....0....0....0....0....0....0....0....0
%e A243514 ..1....0....0....0....1....1....1....1....0....0
%e A243514 ..2....1....0....1....2....2....2....2....0....0
%e A243514 ..0....2....1....2....3....3....3....0....0....0
%e A243514 ..1....0....2....3....1....0....4....3....1....0
%Y A243514 Column 5 of A243519.
%K A243514 nonn
%O A243514 1,1
%A A243514 _R. H. Hardin_, Jun 05 2014