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A218479
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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.
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2
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1, 1, 25, 817, 30345, 1215521, 51186169, 2233558545, 100094682729, 4579454148865, 213011954187225, 10043235050384625, 478897402022246985, 23054568307757054433, 1118987674598361862585, 54698321862693296502737, 2690410083349269351772713
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
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FORMULA
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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
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MAPLE
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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);
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CROSSREFS
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Column k=9 of A213027.
Sequence in context: A132540 A337247 A142998 * A183879 A246761 A122142
Adjacent sequences: A218476 A218477 A218478 * A218480 A218481 A218482
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 29 2012
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STATUS
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approved
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