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A121482 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. 2
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; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Column 0 of A121481.
LINKS
E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, Nondecreasing Dyck paths and q-Fibonacci numbers, Discrete Math., 170, 1997, 211-217.
FORMULA
G.f.: (1-z-z^2)(1-2z^2)/(1-z-4z^2+2z^3+4z^4-z^6).
EXAMPLE
a(4)=3 because we have UUDDUUDD, UUDUDUDD and UUUUDDDD, where U=(1,1) and D=(1,-1).
MAPLE
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);
CROSSREFS
Cf. A121481.
Sequence in context: A183921 A177143 A191391 * A368858 A013498 A161624
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 02 2006
STATUS
approved

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Last modified April 21 19:32 EDT 2024. Contains 371885 sequences. (Running on oeis4.)