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The k–Fibonacci difference sequences

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  • Falcon, Sergio

Abstract

In this paper we apply the concept of difference relation to the sequences of k–Fibonacci numbers. We will obtain general formulas to find any term of the ith k–Fibonacci difference sequence from the initial k–Fibonacci numbers. We also find formulas for the sum of the elements of these new sequences as well as their generating functions. Finally, we study the k–Fibonacci Newton polynomial interpolation.

Suggested Citation

  • Falcon, Sergio, 2016. "The k–Fibonacci difference sequences," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 153-157.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:153-157
    DOI: 10.1016/j.chaos.2016.03.038
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    References listed on IDEAS

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    1. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    2. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
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