Annals of Combinatorics

Anders, Katherine; Dennison, Melissa; Lansing, Jennifer; Reznick, Bruce

doi: 10.1007/s00026-013-0188-3pmid: N/A

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