A218480 Number of 3n-length 10-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, 28, 1027, 42850, 1929043, 91320022, 4480436836, 225785025802, 11617042380355, 607729841261560, 32227411217273515, 1728444323307664720, 93593058046710649012, 5109705135623767855960, 280954986758729989837624, 15544627425243191634814666

Offset: 0

Author

Alois P. Heinz, Oct 29 2012

Keywords

• nonn

Comments

In general, column k of A213027 is (for k > 1) asymptotic to a(n) ~ 3^(3*n+1/2) * (k-1)^(n+1) / (sqrt(Pi) * (2*k-3)^2 * 4^n * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Column k=10 of A213027.

Programs

Maple

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*9^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)*9^j for n>0, a(0) = 1.

Recurrence: 2*n*(2*n-1)*(13*n-15)*a(n) = (55159*n^3 - 95963*n^2 + 38478*n - 1080)*a(n-1) - 27000*(3*n-5)*(3*n-4)*(13*n-2)*a(n-2). - Vaclav Kotesovec, Aug 31 2014

a(n) ~ 3^(5*n+5/2) / (289 * sqrt(Pi) * 4^n * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014