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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.
2
1, 1, 22, 631, 20546, 721071, 26594464, 1016157668, 39868799482, 1596785816431, 65014851904262, 2683064838415039, 111976833827421368, 4717961282984709124, 200410768873037098384, 8573481927644738115096, 369045717586929668129706, 15972561730958196240953007
OFFSET
0,3
LINKS
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: A092086 A373723 A369142 * A223624 A230836 A137262
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 29 2012
STATUS
approved