For p, q ∈ N, a finite nonempty set F is said to be (p, q)-Schreier (or maximal (p, q)-Schreier, respectively) if q min F ≥ p|F| (or q min F = p|F|, respectively). Using the inclusion-exclusion principle, Beanland et al. proved a linear recurrence for the counts of (p, q)-Schreier sets of the natural numbers. We show that the counts are taken periodically from Padovan-like sequences that satisfy simple recurrence relations. As an application, we obtain an alternative proof of Beanland et al.'s result. Furthermore, a similar result holds for the counts of maximal (p, q)-Schreier sets. We end with a discussion of the relation between (p, q)-Schreier and maximal (p, q)-Schreier sets.