Arithmetic Properties of Partitions with 1 colored Even Parts and r colored Odd Parts

Abstract: Recently, Hirschhorn and Sellers defined the partition function a_r(n), which counts the number of partitions of n wherein even parts come in only one color, while the odd parts may appear in one of r-colors for fixed r greater than or equal to 1. In this paper, we employ an identity of Newman to derive infinite families of congruences modulo 5 for a_3(n), and use arithmetic theory of modular forms to prove congruences modulo 3 and modulo 5 for a_5(n).