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Title: On the Fibonacci k-numbers
Authors: Falcón, Sergio 
Plaza, Ángel 
UNESCO Clasification: 120504 Teoría elemental de los números
Keywords: Golden Section
Triangular Grids
Issue Date: 2007
Project: Mtm2005-08441-C02-02. Particiones Triangulares y Algoritmos de Refinamiento 
Journal: Chaos, Solitons and Fractals 
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.
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2006.09.022
Source: Chaos, Solitons and Fractals [ISSN 0960-0779], v. 32 (5), p. 1615-1624
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