Some new congruences for generalized overcubic partition function

Abstract

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 ${\overline{a}}_{2^{\lambda }m+t}(n)\equiv {\overline{a}}_t(n)(\mathrm{mod}{2}^{\lambda +1})$, where $\lambda \ge 1,m\ge 0,$ and $t\ge 1$ 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.