Odd behavior in the coefficients of reciprocals of binary power series

Abstract

Let A be a finite subset of N including 0 and f A (n) be the numberThe sequence (f A (n)) mod 2 is always periodic, and f A (n) is typically more often even than odd. We give four families of sets (Am) with |Am| = 4 such that the proportion of odd

Counting non-standard binary representations

“…, a z }, with a i ∈ N and a i < a i+1 for all 0 ≤ i ≤ z − 1. For more on this topic, see the author's previous work [1]. We parameterize A in terms of its s even elements and (z + 1) − s := t odd elements as follows:…”