From a Rogers’s identity to overpartitions

Abstract

In this paper, the author provides an efficient linear recurrence relation for the number of partitions of n into parts not congruent to 0, ± 1 , ± 8 , ± 9 and 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.