

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
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OFFSET

0,5


COMMENTS

Column 0 of A121481.


LINKS

Table of n, a(n) for n=0..33.
E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, Nondecreasing Dyck paths and qFibonacci numbers, Discrete Math., 170, 1997, 211217.
Index entries for linear recurrences with constant coefficients, signature (1,4,2,4,0,1).


FORMULA

G.f.: (1zz^2)(12z^2)/(1z4z^2+2z^3+4z^4z^6).


EXAMPLE

a(4)=3 because we have UUDDUUDD, UUDUDUDD and UUUUDDDD, where U=(1,1) and D=(1,1).


MAPLE

G:=(1zz^2)*(12*z^2)/(1z4*z^2+2*z^3+4*z^4z^6): Gser:=series(G, z=0, 40): seq(coeff(Gser, z, n), n=0..37);


CROSSREFS

Cf. A121481.
Sequence in context: A183921 A177143 A191391 * A013498 A161624 A247794
Adjacent sequences: A121479 A121480 A121481 * A121483 A121484 A121485


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Aug 02 2006


STATUS

approved



