A218475 Number of 3n-length 5-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, 13, 217, 4085, 82593, 1751197, 38413481, 864413317, 19842830065, 462825376685, 10937407206265, 261311076852245, 6301225556698177, 153160687795008445, 3748598210810053449, 92303640047399410341, 2285025852515378528913, 56836898766186234593485

Offset: 0

Author

Alois P. Heinz, Oct 29 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250

Crossrefs

Column k=5 of A213027.

Programs

Maple

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*4^j, j=0..n-1)/n):
seq(a(n), n=0..20);

Formula

a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*4^j for n>0, a(0) = 1.

Recurrence: n*(2*n-1)*(4*n-5)*a(n) = (1216*n^3 - 2452*n^2 + 1267*n - 120)*a(n-1) - 750*(3*n-5)*(3*n-4)*(4*n-1)*a(n-2). - Vaclav Kotesovec, Aug 31 2014

a(n) ~ 4 * 3^(3*n+1/2) / (49 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014