Generation of Dyck paths with increasing peaks. (Génération de chemins de Dyck à pics croissants.) (French) Zbl 0994.05005
This paper gives an algorithm or generating function which enumerates Dyck paths with increasing peaks. A similar generating function is obtained for Dyck paths with decreasing valleys. It is shown that the number of such type of path is asymptotically proportional to \(({3+\sqrt 5\over 2})^n\) with different multiplying constants.
Reviewer: H.N.V.Temperley (Langport)
MSC:
| 05A15 | Exact enumeration problems, generating functions |
Online Encyclopedia of Integer Sequences:
a(n) = 3*a(n-1) - a(n-2) for n >= 2, with a(0) = a(1) = 1.Number of Dyck paths of length 2n with nondecreasing peaks.
Triangle read by rows: T(n,k) is the number of Dyck paths with nondecreasing peaks having semilength n and with height of last peak equal to k (1 <= k <= n).
Decimal expansion of a constant related to A048285.
