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A243516 Number of length n+2 0..7 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..7 introduced in 0..7 order. 1

%I

%S 3,5,10,25,77,280,1156,5267,25915,135214,736706,4139833,23767897,

%T 138468212,814675840,4824766303,28699128503,171207852154,

%U 1023332115838,6124430348357,36684624841813,219860794899520,1318179574171580

%N Number of length n+2 0..7 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..7 introduced in 0..7 order.

%H R. H. Hardin, <a href="/A243516/b243516.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-1) - 111*a(n-2) + 355*a(n-3) - 584*a(n-4) + 468*a(n-5) - 144*a(n-6).

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

%F G.f.: x*(3 - 46*x + 258*x^2 - 655*x^3 + 739*x^4 - 288*x^5) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 6*x)).

%F a(n) = (2722 + 675*2^n + 25*2^(1+2*n) + 50*3^(1+n) + 2^n*3^(1+n) + 660*n) / 1800.

%F (End)

%e All solutions for n=3:

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

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

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

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

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

%Y Column 7 of A243519.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 05 2014

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)