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%I #11 Oct 23 2015 12:20:47
%S 1,1,16,331,7746,195011,5153626,140995716,3958980906,113434797571,
%T 3303283462836,97478710394451,2908594804576416,87605427983818356,
%U 2659959016770389896,81330226479826092536,2501989790308939894026,77386492111973937031491,2405093253522796180052056
%N Number of 3n-length 6-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
%H Alois P. Heinz, <a href="/A218476/b218476.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*5^j for n>0, a(0) = 1.
%F Recurrence: 2*n*(2*n-1)*(9*n-11)*a(n) = 3*(2997*n^3 - 5769*n^2 + 2754*n - 200)*a(n-1) - 3240*(3*n-5)*(3*n-4)*(9*n-2)*a(n-2). - _Vaclav Kotesovec_, Aug 31 2014
%F a(n) ~ 3^(3*n-7/2) * 5^(n+1) / (sqrt(Pi) * n^(3/2) * 4^n). - _Vaclav Kotesovec_, Aug 31 2014
%p a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*5^j, j=0..n-1)/n):
%p seq(a(n), n=0..20);
%Y Column k=6 of A213027.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Oct 29 2012
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