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.

1, 1, 22, 631, 20546, 721071, 26594464, 1016157668, 39868799482, 1596785816431, 65014851904262, 2683064838415039, 111976833827421368, 4717961282984709124, 200410768873037098384, 8573481927644738115096, 369045717586929668129706, 15972561730958196240953007

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*7^j for n>0, a(0) = 1.

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

a(n) ~ 3^(3*n+1/2) * 7^(n+1) / (169 * sqrt(Pi) * 4^n * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014

Maple

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*7^j, j=0..n-1)/n):
seq(a(n), n=0..20);

Crossrefs

Column k=8 of A213027.

Sequence in context: A084271 A092086 A369142 * A223624 A230836 A137262

Adjacent sequences: A218475 A218476 A218477 * A218479 A218480 A218481

Keyword

nonn

Author

Alois P. Heinz, Oct 29 2012

Status

approved