  Rowland and Zeilberger devised an approach to algorithmically determine the
modulo $p^r$ reductions of values of combinatorial sequences representable as
constant terms (building on work of Rowland and Yassawi). The resulting
$p$-schemes are systems of recurrences and, depending on their shape, are
classified as automatic or linear. We revisit this approach, provide some
additional details such as bounding the number of states, and suggest a third
natural type of scheme that combines benefits of automatic and linear ones. We
illustrate the utility of these "scaling" schemes by confirming and extending a
conjecture of Rowland and Yassawi on Motzkin numbers.
