Journal of Integer Sequences, Vol. 26 (2023), Article 23.4.7

On Motzkin-Schröder Paths, Riordan Arrays, and Somos-4 Sequences

Paul Barry
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.

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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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