On Enumeration of Dyck Paths with Colored Hills
Department of Mathematics and Informatics
University of Banja Luka
Banja Luka, 78000
Republic of Srpska, BA
We continue to investigate the properties of the earlier defined functions
which depend on an initial arithmetic function f0
. In this
paper, values of f0
are the Fine numbers.
We investigate functions fi
= 1, 2, 3, 4),
and show that these functions count Dyck paths
having hills in different colors. For each function, we also derive an
explicit formula. We also prove several results which mutually connect
these functions. It appears that
well-known objects called the Catalan triangles.
We finish with two identities relating different kind of combinatorial objects.
Full version: pdf,
(Concerned with sequences
Received May 29 2018; revised version received October 18 2018.
Published in Journal of Integer Sequences, December 13 2018.
Journal of Integer Sequences home page