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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.

%I A243516 #8 Nov 02 2018 12:26:30
%S A243516 3,5,10,25,77,280,1156,5267,25915,135214,736706,4139833,23767897,
%T A243516 138468212,814675840,4824766303,28699128503,171207852154,
%U A243516 1023332115838,6124430348357,36684624841813,219860794899520,1318179574171580
%N 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.
%H A243516 R. H. Hardin, <a href="/A243516/b243516.txt">Table of n, a(n) for n = 1..210</a>
%F A243516 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 A243516 Conjectures from _Colin Barker_, Nov 02 2018: (Start)
%F A243516 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 A243516 a(n) = (2722 + 675*2^n + 25*2^(1+2*n) + 50*3^(1+n) + 2^n*3^(1+n) + 660*n) / 1800.
%F A243516 (End)
%e A243516 All solutions for n=3:
%e A243516 ..0....0....0....0....0....0....0....0....0....0
%e A243516 ..0....0....0....1....0....1....1....1....0....1
%e A243516 ..1....0....0....2....1....2....2....2....0....2
%e A243516 ..2....0....1....3....2....3....0....3....0....0
%e A243516 ..3....1....2....0....0....4....3....1....0....1
%Y A243516 Column 7 of A243519.
%K A243516 nonn
%O A243516 1,1
%A A243516 _R. H. Hardin_, Jun 05 2014