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Search: id:A121483
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| A121483 |
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Number of peaks at odd level in all nondecreasing Dyck paths of semilength n. 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
3
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| 1, 2, 6, 19, 56, 167, 487, 1411, 4047, 11527, 32617, 91790, 257065, 716896, 1991792, 5515535, 15227846, 41930133, 115176023, 315676425, 863475561, 2357539227, 6425887551, 17487572124, 47522431681, 128969086382, 349567320762
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)=Sum(k*A121481(n,k),k=0..n).
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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)(1-3z+6z^3-3z^4)/[(1+z)(1-3z+z^2)^2*(1-z-z^2)].
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EXAMPLE
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a(2)=2 because in UDUD and UUDD we have altogether 2 peaks at odd level; here U=(1,1) and D=(1,-1).
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MAPLE
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G:=z*(1-z)*(1-3*z+6*z^3-3*z^4)/(1+z)/(1-3*z+z^2)^2/(1-z-z^2): Gser:=series(G, z=0, 33): seq(coeff(Gser, z, n), n=1..30);
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CROSSREFS
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Cf. A121481, A121486, A038731.
Sequence in context: A034533 A014559 A027098 this_sequence A077834 A067675 A037512
Adjacent sequences: A121480 A121481 A121482 this_sequence A121484 A121485 A121486
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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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