From a Rogers’s identity to overpartitions

In this paper, the author provides an efficient linear recurrence relation for the number of partitions of n into parts not congruent to 0, $$\pm 1$$±1, $$\pm 8$$±8, $$\pm 9$$±9 and $$10 \pmod {20}$$10(mod20). A simple criterion for deciding whether this number is odd or even is given as a corollary of this result. Some results involving overpartitions and partitions into distinct parts have been derived in this context.