cp's OEIS Frontend

A218479 Number of 3n-length 9-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 A218479 #11 Oct 23 2015 12:20:00
%S A218479 1,1,25,817,30345,1215521,51186169,2233558545,100094682729,
%T A218479 4579454148865,213011954187225,10043235050384625,478897402022246985,
%U A218479 23054568307757054433,1118987674598361862585,54698321862693296502737,2690410083349269351772713
%N A218479 Number of 3n-length 9-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 A218479 Alois P. Heinz, <a href="/A218479/b218479.txt">Table of n, a(n) for n = 0..200</a>
%F A218479 a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*8^j for n>0, a(0) = 1.
%F A218479 Recurrence: n*(2*n-1)*(6*n-7)*a(n) = 3*(3132*n^3 - 5544*n^2 + 2289*n - 80)*a(n-1) - 8748*(3*n-5)*(3*n-4)*(6*n-1)*a(n-2). - _Vaclav Kotesovec_, Aug 31 2014
%F A218479 a(n) ~ 2^(n+3) * 3^(3*n-3/2) / (25 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Aug 31 2014
%p A218479 a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*8^j, j=0..n-1)/n):
%p A218479 seq(a(n), n=0..20);
%Y A218479 Column k=9 of A213027.
%K A218479 nonn
%O A218479 0,3
%A A218479 _Alois P. Heinz_, Oct 29 2012