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A243637 Number of length n+2 0..6 arrays with no three unequal elements in a row and new values 0..6 introduced in 0..6 order.

%I A243637 #7 Nov 02 2018 10:34:25
%S A243637 4,9,21,51,127,324,844,2243,6073,16737,46905,133555,386047,1131958,
%T A243637 3364454,10129563,30871733,95176427,296618011,933821451,2967726939,
%U A243637 9514201392,30747183016,100097739315,328049191105,1081610514581
%N A243637 Number of length n+2 0..6 arrays with no three unequal elements in a row and new values 0..6 introduced in 0..6 order.
%H A243637 R. H. Hardin, <a href="/A243637/b243637.txt">Table of n, a(n) for n = 1..210</a>
%F A243637 Empirical: a(n) = 11*a(n-1) - 39*a(n-2) + 21*a(n-3) + 151*a(n-4) - 217*a(n-5) - 181*a(n-6) + 339*a(n-7) + 130*a(n-8) - 154*a(n-9) - 60*a(n-10).
%F A243637 Empirical g.f.: x*(4 - 35*x + 78*x^2 + 87*x^3 - 408*x^4 - 16*x^5 + 668*x^6 + 57*x^7 - 368*x^8 - 120*x^9) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 5*x^2)). - _Colin Barker_, Nov 02 2018
%e A243637 Some solutions for n=6:
%e A243637 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A243637 ..1....1....0....1....1....0....0....0....1....1....1....1....1....1....1....1
%e A243637 ..1....0....1....1....1....1....0....1....1....1....1....0....0....1....1....1
%e A243637 ..2....0....1....0....1....0....1....1....1....1....2....0....1....2....0....0
%e A243637 ..1....1....1....0....0....0....1....0....2....2....2....1....1....2....0....1
%e A243637 ..2....1....1....0....1....1....2....1....2....2....2....0....0....2....2....1
%e A243637 ..2....2....2....0....0....0....2....0....1....2....3....0....0....1....0....1
%e A243637 ..1....2....2....1....0....0....0....0....1....1....2....2....2....2....0....2
%Y A243637 Column 6 of A243641.
%K A243637 nonn
%O A243637 1,1
%A A243637 _R. H. Hardin_, Jun 08 2014