This compendium uncovers generating functions for 15 types of Motzkin-like paths, highlighting new circular variants. It employs the symbolic method for comprehensive analysis.
We catalog fifteen types of Motzkin-like paths with various restrictions and use the symbolic method to determine their generating functions, several of which are new. We also introduce a new type of Motzkin path corresponding to a walk on a circle, rather than on a line.
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Jacob Vogelpohl (2025) studied this question.
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