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

Author

Emeric Deutsch, Aug 02 2006

Keywords

• nonn

Comments

Column 0 of A121481.

Examples

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

Links

• 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).

Crossrefs

Cf. A121481.

Programs

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);

Formula

G.f.: (1-z-z^2)(1-2z^2)/(1-z-4z^2+2z^3+4z^4-z^6).