On the Fibonacci k-numbers

Sergio Falcón and Ángel Plaza

Chaos, Solitons & Fractals, 2007, vol. 32, issue 5, 1615-1624

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:32:y:2007:i:5:p:1615-1624

DOI: 10.1016/j.chaos.2006.09.022

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