On Log-Definite Tempered Combinatorial Sequences

Tomislav Došlić and Biserka Kolarec ()
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Tomislav Došlić: Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kačićeva ulica 26, 10 000 Zagreb, Croatia
Biserka Kolarec: Department of Information Science and Mathematics, Faculty of Agriculture, University of Zagreb, Svetošimunska cesta 25, 10 000 Zagreb, Croatia

Mathematics, 2025, vol. 13, issue 7, 1-19

Abstract: This article is concerned with qualitative and quantitative refinements of the concepts of the log-convexity and log-concavity of positive sequences. A new class of tempered sequences is introduced, its basic properties are established and several interesting examples are provided. The new class extends the class of log-balanced sequences by including the sequences of similar growth rates, but of the opposite log-behavior. Special attention is paid to the sequences defined by two- and three-term linear recurrences with constant coefficients. For the special cases of generalized Fibonacci and Lucas sequences, we graphically illustrate the domains of their log-convexity and log-concavity. For an application, we establish the concyclicity of the points a 2 n a 2 n + 1 , 1 a 2 n + 1 for some classes of Horadam sequences ( a n ) with positive terms.

Keywords: tempered sequence; log-convexity; log-concavity; log-balancedness; Fibonacci numbers; Lucas numbers; concyclic points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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