Unimodality and log-concavity of generalized Glasby-Paseman sequences

In this paper, we consider a two-parameter ($l$ and $a$) generalization of a sequence that Glasby and Paseman considered. Based on computer experiments, we conjecture its unimodality, log-concavity, peak positions, and the asymptotic behavior of the maximum values. Then we prove this conjecture for the case where $l=2$ and $a=1$. We finish the paper by making some comments about the conjecture on the generalized sequence.