Some new congruences for generalized overcubic partition function

Amdeberhan et al. (2024) introduced the notion of a generalized overcubic partition function $\overline a_c (n)$ and proved an infinite family of congruences modulo a prime $p\ge 3$ and some Ramanujan type congruences. In this paper, we show that $\overline a_{2^\lambda m+t}(n) \equiv \overline a_t (n) \pmod {2^{\lambda+1}}$, where $\lambda \geq1, m\geq0,$ and $t\geq1$ are integers. We also prove some new congruences modulo $8$ and $16$ for $\overline a_{2m+1}(n), \overline a_{2m+2}(n), \overline a_{8m+3}(n)$, where $m$ is any non-negative integer.