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On Log-Definite Tempered Combinatorial Sequences

Author

Listed:
  • Tomislav Došlić

    (Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kačićeva ulica 26, 10 000 Zagreb, Croatia)

  • Biserka Kolarec

    (Faculty of Agriculture, Department of Information Science and Mathematics, University of Zagreb, Svetošimunska cesta 25, 10 000 Zagreb, Croatia)

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.

Suggested Citation

  • Tomislav Došlić & Biserka Kolarec, 2025. "On Log-Definite Tempered Combinatorial Sequences," Mathematics, MDPI, vol. 13(7), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1179-:d:1627202
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