Congruence properties of binary partition functions

Abstract

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 $\sum e_j{2}^j$, 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.

References in corpus (1)

• Regularity properties of the Stern enumeration of the rationals