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

0,3

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

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

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);

Crossrefs

Column k=10 of A213027.

Sequence in context: A034904 A189995 A228689 * A162006 A365029 A370358

Adjacent sequences: A218477 A218478 A218479 * A218481 A218482 A218483

Keyword

nonn

Author

Alois P. Heinz, Oct 29 2012

Status

approved