An infinite family of congruences modulo for -regular bipartitions

Let B-13(n) denote the number of 13-regular bipartitions of n. Our goal is to consider this function from an arithmetical point of view in the spirit of Ramanujan's congruences for the unrestricted partition function p(n). In particular, we shall prove an infinite family of congruences: for alpha >= 2 and n >= 0, B-13(3(alpha)n + 2 . 3(alpha-1) - 1) equivalent to 0 (mod 3). In addition, we will also give an alternative proof of one infinite family of congruences for b(13)(n), the number of 13 regular partitions of n, due to Webb.