A218477 Number of 3n-length 7-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, 19, 469, 13123, 395461, 12517939, 410380885, 13811907043, 474457464613, 16567069507219, 586287339402997, 20980966876537411, 757961579781924805, 27605221102084999411, 1012488016842242735509, 37364825362229946450595, 1386427393386051832383589

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

Recurrence: n*(2*n-1)*(5*n-6)*a(n) = (3835*n^3 - 7127*n^2 + 3201*n - 180)*a(n-1) - 3087*(3*n-5)*(3*n-4)*(5*n-1)*a(n-2). - Vaclav Kotesovec, Aug 31 2014

a(n) ~ 3^(4*n+3/2) / (121 * 2^(n-1) * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014

Maple

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*6^j, j=0..n-1)/n):
seq(a(n), n=0..20);

Crossrefs

Column k=7 of A213027.

Sequence in context: A284197 A081686 A284163 * A003700 A093975 A159248

Adjacent sequences: A218474 A218475 A218476 * A218478 A218479 A218480

Keyword

nonn

Author

Alois P. Heinz, Oct 29 2012

Status

approved