On 3-Regular Partitions in 3-Colors

We consider p({3,3})(n), the number of 3-regular partitions in 3-colors. We find the generating functions for p({3,3})(n) and deduce congruences modulo large powers of 3. We also find the generating functions and congruences for linear combination of p(3)(n) (the number of partitions of n in 3-colors) by finding the relation connecting p(3)(n) and p({3,3})(n). As an application, we find finite discrete convolution of p({3,1})(n) and p({3,2})(n).