In recent work, Amdeberhan and Merca considered the integer partition function a (n) which counts the number of integer partitions of weight n wherein even parts come in only one color (i. e. , they are monochromatic), while the odd parts may appear in one of three colors. One of the results that they proved was that, for all n 0, a (7n+2) 0 7. In this work, we generalize this function a (n) by naturally placing it within an infinite family of related partition functions. Using elementary generating function manipulations and classical q--series identities, we then prove infinitely many congruences modulo 7 which are satisfied by members of this family of functions.
Hirschhorn et al. (Sun,) studied this question.