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Search: id:A098075
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| A098075 |
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Threefold convolution of A004148 (the RNA secondary structure numbers) with itself. |
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1
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| 1, 3, 6, 13, 30, 69, 160, 375, 885, 2102, 5022, 12060, 29095, 70485, 171399, 418220, 1023663, 2512761, 6184253, 15257262, 37725972, 93477778, 232069116, 577179078, 1437926977, 3587977293, 8966170056, 22437282917, 56221762626, 141051397725
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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I. L. Hofacker, P. Schuster, and P. F. Stadler, Combinatorics of RNA secondary structures, Discrete Appl. Math., 88, 1998, 207-237.
P. R. Stein and M. S. Waterman, On some new sequences generalizing the Catalan and Motzkin numbers, Discrete Math., 26, 1979, 261-272.
M. Vauchassade de Chaumont and G. Viennot, Polynomes orthogonaux et problemes d'enumeration en biologie moleculaire, Publ. I.R.M.A. Strasbourg, 1984, 229/S-08, Actes 8e Sem. Lotharingien, pp. 79-86.
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LINKS
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M. Vauchassade de Chaumont and G. Viennot, Polynomes orthogonaux at problemes d'enumeration en biologie moleculaire, Sem. Loth. Comb. B08l (1984) 79-86.
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FORMULA
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a(n)=3sum(binomial(k, n-k)*binomial(k+2, 3+n-k)/k, k=ceil((n+1)/2)..n) (n>=1), a(0)=1. G.f. = f^3, where f=[1-z+z^2-sqrt(1-2z-z^2-2z^3+z^4)]/(2z^2) is the g.f. of A004148.
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MAPLE
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a:=proc(n) if n=0 then 1 else 3*sum(binomial(k, n-k)*binomial(k+2, 3+n-k)/k, k=ceil((n+1)/2)..n) fi end: seq(a(n), n=0..30);
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CROSSREFS
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Cf. A004148.
Adjacent sequences: A098072 A098073 A098074 this_sequence A098076 A098077 A098078
Sequence in context: A005313 A108639 A087218 this_sequence A137584 A125267 A141353
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 13 2004
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