Some congruences modulo 3, 5 and 7 for broken ((rl-1)/2)-diamond partitions for r ∈ {3,25,49} and odd positive integer l

For any non negative integer n and a fixed positive integer k, let Delta(k)(n) denote the number of broken k-diamond partitions of n. In this paper, we prove some congruences modulo 3 for Delta((3l-1)/2)(n), modulo 5 for Delta((25l-1)/2)(n), and modulo 7 for Delta((49l-1)/2)(n), for odd positive integer l. We also prove a new congruence modulo 5 for Delta(2)(n). (C) 2017 Elsevier Inc. All rights reserved.