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Let pₒ (n) denote the number of overpartitions of n into odd parts. The partition function pₒ (n) has been the subject of many recent studies where many explicit Ramanujan-like congruences were discovered. In this paper, we provide three linear recurrence relation for pₒ (n). Several connections with partitions into parts not congruent to 2 4, overpartitions and partitions into distinct parts are presented in this context.
Deepthi et al. (Sat,) studied this question.