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.

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

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 q-Fibonacci numbers, Discrete Math., 170, 1997, 211-217.

Index entries for linear recurrences with constant coefficients, signature (1,4,-2,-4,0,1).

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

Adjacent sequences: A121479 A121480 A121481 * A121483 A121484 A121485

Keyword

nonn

Author

Emeric Deutsch, Aug 02 2006

Status

approved