New generalization of cubic partition of $n$

Abstract

Let $c^*_{(1,r,a)}(n)$ be the generalization of the cubic partition function $c(n)$. In this paper, we prove some new congruences modulo odd prime $p$ by taking $r=3,4,5,7,11$ and $13$ using $q$-series identities. We study congruence properties of generalization of cubic partition function for different values of $a$ and give some particular cases as examples.