Peakless Motzkin paths of bounded height
Abstract
There was recent interest in Motzkin paths without peaks (peak: up-step followed immediately by down-step); additional results about this interesting family is worked out. The new results are the enumeration of such paths that live in a strip [0..], and as consequence the asymptotics of the average height, which is given by 2· 5-1/4π n. Methods include the kernel method and singularity analysis of generating functions.
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