cp's OEIS Frontend

A218472 Number of 3n-length n-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.

%I A218472 #12 Mar 25 2016 13:13:54
%S A218472 1,1,4,61,1810,82593,5153626,410380885,39868799482,4579454148865,
%T A218472 607729841261560,91553310170011501,15441283593044256696,
%U A218472 2883254656878648757729,590578881927993264483880,131681888589427990097216549,31753512197914767223878851626
%N A218472 Number of 3n-length n-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 A218472 Alois P. Heinz, <a href="/A218472/b218472.txt">Table of n, a(n) for n = 0..150</a>
%F A218472 a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*(n-1)^j for n>1, a(n) = 1 else.
%F A218472 a(n) ~ 3^(3*n + 1/2) * n^(n - 5/2) / (sqrt(Pi) * exp(1) * 2^(2*n+2)). - _Vaclav Kotesovec_, Mar 25 2016
%p A218472 a:= n-> `if`(n<2, 1, add(binomial(3*n, j)*(n-j)*(n-1)^j, j=0..n-1)/n):
%p A218472 seq(a(n), n=0..20);
%Y A218472 Diagonal of A213027.
%K A218472 nonn
%O A218472 0,3
%A A218472 _Alois P. Heinz_, Oct 29 2012