Behavior of digital sequences through exotic numeration systems

Many digital functions studied in the literature, e.g., the summatory function
of the base-k sum-of-digits function, have a behavior showing some periodic fluctuation.
Such functions are usually studied using techniques from analytic number
theory or linear algebra. In this paper we develop a method based on exotic numeration
systems and we apply it on two examples motivated by the study of generalized
Pascal triangles and binomial coefficients of words.