In this paper, we establish the combinatorial interpretations of the hyper-Leonardo numbers Leₙ^ (r) and Leonardo numbers Leₙ. We investigate the log-concavity of the Leonardo numbers for n 3 and the hyper-Leonardo numbers for n, r 1. In addition, we prove the log-balancedness of the hyper-Leonardo numbers for r = 1, 2. Furthermore, we prove the q -log-concavity of the polynomial ₊=₀ⁿ Leₖ^ (r) qᵏ for n, r 1.
Rezig et al. (Wed,) studied this question.