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A194727
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Number of 7-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
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3
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1, 1, 13, 205, 3565, 65821, 1265677, 25066621, 507709165, 10466643805, 218878998733, 4631531585341, 98980721277613, 2133274258946845, 46313701181477005, 1011889827742935805, 22232378278653590125, 490899296804667191005, 10887346288742800406605
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history;
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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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G.f.: 6/7 + 12/(7*(5+7*sqrt(1-24*x))).
a(0) = 1, a(n) = 1/n * Sum_{j=0..n-1} C(2*n,j)*(n-j)*6^j for n>0.
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EXAMPLE
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a(2) = 13: aaaa, aabb, aacc, aadd, aaee, aaff, aagg, abba, acca, adda, aeea, affa, agga (with 7-ary alphabet {a,b,c,d,e,f,g}).
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MAPLE
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a:= n-> `if` (n=0, 1, add (binomial (2*n, j) *(n-j) *6^j, j=0..n-1) /n):
seq (a(n), n=0..20);
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CROSSREFS
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Column k=7 of A183134.
Sequence in context: A057807 A057804 A215621 * A059355 A206348 A145270
Adjacent sequences: A194724 A194725 A194726 * A194728 A194729 A194730
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Sep 02 2011
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STATUS
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approved
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