Investigates combinatorial aspects and positivities of hyper-Leonardo and Leonardo numbers, indicating deeper mathematical insights.
In this paper, we establish the combinatorial interpretations of the hyper-Leonardo numbers Le_n⁽ʳ⁾ and Leonardo numbers Le_n . 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 ∑ₖ₌₀^n Le_k⁽ʳ⁾ q^k for n, r ≥ 1 .
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Rezig et al. (2025) studied this question.
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