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

0,3

Links

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

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

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);

Crossrefs

Column k=5 of A213027.

Sequence in context: A069989 A140517 A096141 * A294982 A320627 A059525

Adjacent sequences: A218472 A218473 A218474 * A218476 A218477 A218478

Keyword

nonn

Author

Alois P. Heinz, Oct 29 2012

Status

approved