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 $k \leq n/4$.
Partition function, pentagonal number theorem, recurrence relation
"New recurrences for Euler's partition function,"
Turkish Journal of Mathematics: Vol. 41:
5, Article 10.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss5/10