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A243513 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. 1

%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(n-1) - 7*a(n-2) + 3*a(n-3).

%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

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Last modified July 25 12:15 EDT 2021. Contains 346290 sequences. (Running on oeis4.)