More infinite families of congruences modulo 5 for broken 2-diamond partitions

The notion of broken k  -diamond partitions was introduced by Andrews and Paule. Let Δk(n)Δk(n) denote the number of broken k-diamond partitions of n for a fixed positive integer k  . Recently, Chan, and Paule and Radu proved some congruences modulo 5 for Δ2(n)Δ2(n). In this paper, we prove several new infinite families of congruences modulo 5 for Δ2(n)Δ2(n) by using an identity due to Newman. Our results generalize the congruences proved by Paule and Radu.