A conjecture of Radu and Sellers on congruences modulo powers of 2 for broken 3-diamond partitions

Abstract

In 2007, Andrews and Paule introduced the family of functions $\Delta_k(n)$, which enumerate the number of broken $k$-diamond partitions for a fixed positive integer $k$. In 2013, Radu and Sellers completely characterized the parity of $\Delta_3(8n+r)$ for certain values of $r$ and proposed a conjecture on congruences modulo powers of $2$ for broken $3$-diamond partitions. In this paper, we employ an unconventional $U$-sequence to resolve the revised conjecture put forward by Radu and Sellers.