We construct a two-layered model for learning and generating sequential data that is both computationally fast and competitive with vanilla Tsetlin machines, adding numerous advantages. Through the use of hyperdimensional vector computing (HVC) algebras and Tsetlin machine clause structures, we demonstrate that the combination of both inherits the generality of data encoding and decoding of HVC with the fast interpretable nature of Tsetlin machines to yield a powerful machine learning model. We apply the approach in two areas, namely in forecasting, generating new sequences, and classification. For the latter, we derive results for the entire UCR Time Series Archive and compare with the standard benchmarks to see how well the method competes in time series classification.