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 A218479 Number of 3n-length 9-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, 25, 817, 30345, 1215521, 51186169, 2233558545, 100094682729, 4579454148865, 213011954187225, 10043235050384625, 478897402022246985, 23054568307757054433, 1118987674598361862585, 54698321862693296502737, 2690410083349269351772713 (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)*8^j for n>0, a(0) = 1. Recurrence: n*(2*n-1)*(6*n-7)*a(n) = 3*(3132*n^3 - 5544*n^2 + 2289*n - 80)*a(n-1) - 8748*(3*n-5)*(3*n-4)*(6*n-1)*a(n-2). - Vaclav Kotesovec, Aug 31 2014 a(n) ~ 2^(n+3) * 3^(3*n-3/2) / (25 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Aug 31 2014 MAPLE a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*8^j, j=0..n-1)/n): seq(a(n), n=0..20); CROSSREFS Column k=9 of A213027. Sequence in context: A132540 A337247 A142998 * A183879 A246761 A122142 Adjacent sequences: A218476 A218477 A218478 * A218480 A218481 A218482 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 29 2012 STATUS approved

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Last modified March 28 08:48 EDT 2023. Contains 361584 sequences. (Running on oeis4.)