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On the Fibonacci k-numbers

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  • Falcón, Sergio
  • Plaza, Ángel

Abstract

We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers {Fk,n}n=0∞ were found by studying the recursive application of two geometrical transformations used in the well-known four-triangle longest-edge (4TLE) partition. Many properties of these numbers are deduce directly from elementary matrix algebra.

Suggested Citation

  • Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:5:p:1615-1624
    DOI: 10.1016/j.chaos.2006.09.022
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    References listed on IDEAS

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    1. Stakhov, Alexey & Rozin, Boris, 2006. "The continuous functions for the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1014-1025.
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