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On ( k , p )-Fibonacci Numbers

Author

Listed:
  • Natalia Bednarz

    (The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland)

Abstract

In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously. We prove some identities which generalize well-known relations for Fibonacci numbers, Pell numbers and their generalizations. A matrix representation for generalized Fibonacci numbers is given, too.

Suggested Citation

  • Natalia Bednarz, 2021. "On ( k , p )-Fibonacci Numbers," Mathematics, MDPI, vol. 9(7), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:727-:d:525547
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    References listed on IDEAS

    as
    1. Urszula Bednarz & Iwona Włoch & Małgorzata Wołowiec-Musiał, 2015. "Total Graph Interpretation of the Numbers of the Fibonacci Type," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-7, October.
    2. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    3. Kilic, E. & Stakhov, A.P., 2009. "On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2210-2221.
    4. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
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