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A218477 Number of 3n-length 7-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, 19, 469, 13123, 395461, 12517939, 410380885, 13811907043, 474457464613, 16567069507219, 586287339402997, 20980966876537411, 757961579781924805, 27605221102084999411, 1012488016842242735509, 37364825362229946450595, 1386427393386051832383589 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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)*6^j for n>0, a(0) = 1.

Recurrence: n*(2*n-1)*(5*n-6)*a(n) = (3835*n^3 - 7127*n^2 + 3201*n - 180)*a(n-1) - 3087*(3*n-5)*(3*n-4)*(5*n-1)*a(n-2). - Vaclav Kotesovec, Aug 31 2014

a(n) ~ 3^(4*n+3/2) / (121 * 2^(n-1) * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014

MAPLE

a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*6^j, j=0..n-1)/n):

seq(a(n), n=0..20);

CROSSREFS

Column k=7 of A213027.

Sequence in context: A284197 A081686 A284163 * A003700 A093975 A159248

Adjacent sequences:  A218474 A218475 A218476 * A218478 A218479 A218480

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 29 2012

STATUS

approved

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Last modified December 16 04:19 EST 2018. Contains 318158 sequences. (Running on oeis4.)