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 ⩽ n/4