Motzkin paths of bounded height with two forbidden contiguous subwords of length two

Abstract: Motzkin excursions and meanders are revisited. This is considered in the context of forbidden patterns. Previous work by Asinowski, Banderier, Gittenberger, and Roitner is continued. Motzkin paths of bounded height are considered, leading to matrix equations and also to continued fractions. The enumeration is done by properly setting up bivariate generating functions which can be expanded using the kernel method.