New relations for the number of partitions with distinct even parts

Abstract

The number of partitions of n wherein even parts are distinct and odd parts are unrestricted, often denoted by ped(n), has been the subject of many recent studies. In this paper, the author provides an efficient linear recurrence relation for ped(n). A simple criterion for deciding whether ped(n) is odd or even is given as a corollary of this result. Some connections with partitions into parts not congruent to 2(mod4), overpartitions and partitions into distinct parts are presented in this context.