New recurrences for Euler''s partition function

Abstract

In this paper, the author invokes some consequences of the bisectional pentagonal number theorem to derive two linear recurrence relations for Euler's partition function $p(n)$. As a corollary of these results, we obtain an efficient method to compute the parity of Euler's partition function $p(n)$ that requires only the parity of $p(k)$ with $k \leq n/4$.