Motzkin Numbers

  title={Motzkin Numbers},
  author={Robert Donaghey and Louis W. Shapiro},
  journal={J. Comb. Theory, Ser. A},

Congruences for Catalan and Motzkin numbers and related sequences

Some identities on the Catalan, Motzkin and Schröder numbers

Motzkin numbers revisited

Motzkin numbers, like Catalan numbers, have important role in number theory and they preserve their own identity in many ways. In this note we have, as mentioned in the title, have revisited the

Identities involving weighted Catalan, Schröder and Motzkin paths

Taylor expansions for Catalan and Motzkin numbers

Combinatorics of Generalized Motzkin Numbers

The generalized Motzkin numbers are common generalizations of the MotZkin numbers and the Catalan numbers investigated, including the combinatorial interpretation, the recurrence relation, the binomial Transform, the Hankel transform, the log-convexity, the continued fraction of the generating function, and the total positivity of the corresponding Hankel matrix.

Catalan and Motzkin numbers modulo 4 and 8

Catalan Numbers Modulo 2 k

In this paper, we develop a systematic tool to calculate the congruences of some combinatorial numbers involving n!. Using this tool, we re-prove Kummer’s and Lucas’ theorems in a unique concept, and

Walking in the OEIS: From Motzkin numbers to Fibonacci numbers. The "shadows" of Motzkin numbers

In this paper, we consider nine OEIS sequences, the analysis of which allows us to find a connection between Motzkin numbers and Fibonacci numbers. In each Motzkin number, we distinguish an even

Semiorders and Riordan Numbers

In this paper, we define a class of semiorders (or unit interval orders) that arose in the context of polyhedral combinatorics. In the first section of the paper, we will present a pure counting



Restricted plane tree representations of four Motzkin-Catalan equations

Correspondences between plane trees and binary sequences

Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products

This note improves, in two respects, the results of §3.6 of my paper The hyper surface cross ratio. There it is shown that the number cn of independent hypersurface cross ratios that can be formed of

Enumeration of Plane Trees by Branches and Endpoints

Historical Note on a Recurrent Combinatorial Problem

ISSN: 0002-9890 (Print) 1930-0972 (Online) Journal homepage: Historical Note on a Recurrent Combinatorial Problem William G. Brown To cite this article: William

MORSELT, A note on plane trees

  • J. Combinatorial Theory
  • 1967