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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. 2
1, 1, 28, 1027, 42850, 1929043, 91320022, 4480436836, 225785025802, 11617042380355, 607729841261560, 32227411217273515, 1728444323307664720, 93593058046710649012, 5109705135623767855960, 280954986758729989837624, 15544627425243191634814666 (list; graph; refs; listen; history; text; internal format)
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 A025753 A160312

Adjacent sequences: A218477 A218478 A218479 * A218481 A218482 A218483

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 29 2012

STATUS

approved

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Last modified January 31 05:55 EST 2023. Contains 359947 sequences. (Running on oeis4.)