A Note on Overpartition Triples

Abstract

Let n be a positive integer and denotes the number of overpartition triples. In this note, we prove two identities modulo 16 and 32 for . We provide a new method to reprove a result of Lin Wang for completely determining and modulo 16. Also, we find and prove an infinite family of congruences modulo 32 for . The new method relies on expanding the fourth power of the overpartition infinite product together with the help of Gauss' identity.