On Motzkin-Schröder Paths, Riordan Arrays, and Somos-4 Sequences
School of Science
South East Technological University
Building on work by Yang and Gao, we explore links between the
enumeration of lattice paths with steps (1,1), (1,–1), (1,0) and (2,0),
Riordan arrays, continued fractions and a conjectured link to Somos-4
sequences. The study gives insights into the Pascal rhombus and its
Riordan array generalizations. We rely on the A-matrix definition of
Riordan arrays first defined by Merlini, Rogers, Sprugnoli, and Verri
for many of our results.
Full version: pdf,
(Concerned with sequences
Received April 29 2022; revised version received May 3 2023.
Published in Journal of Integer Sequences,
May 9 2023.
Journal of Integer Sequences home page