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.

1, 1, 25, 817, 30345, 1215521, 51186169, 2233558545, 100094682729, 4579454148865, 213011954187225, 10043235050384625, 478897402022246985, 23054568307757054433, 1118987674598361862585, 54698321862693296502737, 2690410083349269351772713

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)*8^j for n>0, a(0) = 1.

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

a(n) ~ 2^(n+3) * 3^(3*n-3/2) / (25 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014

Maple

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*8^j, j=0..n-1)/n):
seq(a(n), n=0..20);

Crossrefs

Column k=9 of A213027.

Sequence in context: A132540 A337247 A142998 * A183879 A246761 A122142

Adjacent sequences: A218476 A218477 A218478 * A218480 A218481 A218482

Keyword

nonn

Author

Alois P. Heinz, Oct 29 2012

Status

approved