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

0,3

Links

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

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

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);

Crossrefs

Diagonal of A213027.

Sequence in context: A229666 A252973 A262654 * A304176 A326225 A102193

Adjacent sequences: A218469 A218470 A218471 * A218473 A218474 A218475

Keyword

nonn

Author

Alois P. Heinz, Oct 29 2012

Status

approved