cp's OEIS Frontend

A218478 Number of 3n-length 8-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 A218478 #10 Oct 23 2015 12:20:23
%S A218478 1,1,22,631,20546,721071,26594464,1016157668,39868799482,
%T A218478 1596785816431,65014851904262,2683064838415039,111976833827421368,
%U A218478 4717961282984709124,200410768873037098384,8573481927644738115096,369045717586929668129706,15972561730958196240953007
%N A218478 Number of 3n-length 8-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 A218478 Alois P. Heinz, <a href="/A218478/b218478.txt">Table of n, a(n) for n = 0..200</a>
%F A218478 a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*7^j for n>0, a(0) = 1.
%F A218478 Recurrence: 2*n*(2*n-1)*(11*n-13)*a(n) = (24607*n^3 - 44503*n^2 + 19066*n - 840)*a(n-1) - 10752*(3*n-5)*(3*n-4)*(11*n-2)*a(n-2). - _Vaclav Kotesovec_, Aug 31 2014
%F A218478 a(n) ~ 3^(3*n+1/2) * 7^(n+1) / (169 * sqrt(Pi) * 4^n * n^(3/2)). - _Vaclav Kotesovec_, Aug 31 2014
%p A218478 a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*7^j, j=0..n-1)/n):
%p A218478 seq(a(n), n=0..20);
%Y A218478 Column k=8 of A213027.
%K A218478 nonn
%O A218478 0,3
%A A218478 _Alois P. Heinz_, Oct 29 2012