On Motzkin-Schröder Paths, Riordan Arrays, and Somos-4 Sequences
Paul Barry
School of Science
South East Technological University
Ireland
Abstract:
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.
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(Concerned with sequences
A000012
A000045
A000108
A001006
A006318
A025235
A059317
A059345
A059398
A059841
A060693
A064189
A071359
A078481
A084782
A085139
A102407
A103210
A128720
A132276
A132277
A143013
A174168
A184019
A190156
A190252
A247333.)
Received April 29 2022; revised version received May 3 2023.
Published in Journal of Integer Sequences,
May 9 2023.
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