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Search: id:A121485
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| A121485 |
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Number of nondecreasing Dyck paths of semilength n and having no peaks at even 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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+0
2
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| 1, 1, 2, 4, 8, 16, 33, 66, 136, 274, 562, 1138, 2327, 4725, 9645, 19613, 39997, 81397, 165906, 337773, 688260, 1401565, 2855432, 5815477, 11846941, 24129498, 49152840, 100116607, 203936639, 415394872, 846143795, 1723513075, 3510704795
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Column 0 of A121484.
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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.=z(1-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)=4 because we have UDUDUDUD, UDUUUDDD, UUUDDDUD and UUUDUDDD, where U=(1,1) and D=(1,-1).
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MAPLE
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G:=z*(1-z^2)*(1-2*z^2)/(1-4*z^2-z+4*z^4-z^6+2*z^3): Gser:=series(G, z=0, 40): seq(coeff(Gser, z, n), n=1..37);
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CROSSREFS
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Cf. A121482, A121484.
Sequence in context: A137181 A036373 A119610 this_sequence A098588 A126683 A005821
Adjacent sequences: A121482 A121483 A121484 this_sequence A121486 A121487 A121488
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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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