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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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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)=Sum(k*A121481(n,k),k=0..n).
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REFERENCES
| 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
| 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
| 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
| 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
| Cf. A121481, A121486, A038731.
Sequence in context: A027098 A183305 A192715 * A077834 A067675 A037512
Adjacent sequences: A121480 A121481 A121482 * A121484 A121485 A121486
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 02 2006
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