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A243635 Number of length n+2 0..4 arrays with no three unequal elements in a row and new values 0..4 introduced in 0..4 order.

%I A243635 #8 Nov 02 2018 11:52:24
%S A243635 4,9,21,51,127,324,844,2242,6062,16655,46411,130937,373349,1074194,
%T A243635 3114146,9085176,26643492,78470989,231925649,687430207,2042284587,
%U A243635 6078844480,18121207896,54086361422,161592030394,483170313579
%N A243635 Number of length n+2 0..4 arrays with no three unequal elements in a row and new values 0..4 introduced in 0..4 order.
%H A243635 R. H. Hardin, <a href="/A243635/b243635.txt">Table of n, a(n) for n = 1..210</a>
%F A243635 Empirical: a(n) = 7*a(n-1) - 14*a(n-2) + 21*a(n-4) - 7*a(n-5) - 6*a(n-6).
%F A243635 Empirical g.f.: x*(4 - 19*x + 14*x^2 + 30*x^3 - 20*x^4 - 12*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)). - _Colin Barker_, Nov 02 2018
%e A243635 Some solutions for n=6:
%e A243635 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A243635 ..0....1....0....1....0....0....0....1....0....1....1....1....0....0....1....1
%e A243635 ..1....1....1....1....1....0....1....1....1....1....0....0....1....1....0....1
%e A243635 ..0....0....1....1....1....0....0....1....0....1....0....1....0....1....1....2
%e A243635 ..1....1....1....1....2....1....0....2....0....0....2....0....0....2....0....1
%e A243635 ..0....1....2....2....2....1....1....2....1....0....2....0....2....2....0....1
%e A243635 ..0....1....1....2....1....1....1....0....1....0....0....0....2....0....0....0
%e A243635 ..2....1....2....3....2....2....0....0....1....0....0....1....2....0....0....0
%Y A243635 Column 4 of A243641.
%K A243635 nonn
%O A243635 1,1
%A A243635 _R. H. Hardin_, Jun 08 2014