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Search: id:A121482
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| A121482 |
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Number of nondecreasing Dyck paths of semilength n and having no peaks at odd level (n>=0). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing. |
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3
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| 1, 0, 1, 1, 3, 5, 12, 22, 49, 94, 201, 396, 828, 1656, 3421, 6899, 14160, 28686, 58672, 119156, 243253, 494688, 1008860, 2053168, 4184892, 8520248, 17361293, 35354517, 72028485, 146696143, 298840769, 608670551, 1239888694, 2525459305
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Column 0 of A121481.
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REFERENCES
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E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, Nondecreasing Dyck paths and q-Fibonacci numbers, Discrete Math., 170, 1997, 211-217.
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FORMULA
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G.f.=(1-z-z^2)(1-2z^2)/(1-z-4z^2+2z^3+4z^4-z^6).
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EXAMPLE
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a(4)=3 because we have UUDDUUDD, UUDUDUDD, and UUUUDDDD, where U=(1,1) and D=(1,-1).
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MAPLE
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G:=(1-z-z^2)*(1-2*z^2)/(1-z-4*z^2+2*z^3+4*z^4-z^6): Gser:=series(G, z=0, 40): seq(coeff(Gser, z, n), n=0..37);
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CROSSREFS
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Cf. A121481.
Sequence in context: A024458 A089292 A034763 this_sequence A013498 A034758 A131322
Adjacent sequences: A121479 A121480 A121481 this_sequence A121483 A121484 A121485
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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), Aug 02 2006
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