  Let A be a finite subset of the natural numbers containing 0, and let f(n)
denote the number of ways to write n in the form $\sum e_j2^j$, where $\e_j \in
A$. We show that there exists a computable T = T(A) so that the sequence (f(n)
mod 2) is periodic with period T. Variations and generalizations of this
problem are also discussed.
