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.

1, 1, 4, 61, 1810, 82593, 5153626, 410380885, 39868799482, 4579454148865, 607729841261560, 91553310170011501, 15441283593044256696, 2883254656878648757729, 590578881927993264483880, 131681888589427990097216549, 31753512197914767223878851626

Offset: 0

Author

Alois P. Heinz, Oct 29 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Diagonal of A213027.

Programs

Maple

a:= n-> `if`(n<2, 1, add(binomial(3*n, j)*(n-j)*(n-1)^j, j=0..n-1)/n):
seq(a(n), n=0..20);

Formula

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.

a(n) ~ 3^(3*n + 1/2) * n^(n - 5/2) / (sqrt(Pi) * exp(1) * 2^(2*n+2)). - Vaclav Kotesovec, Mar 25 2016