On the Fibonacci k-numbers |
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| Authors: | Sergio Falc n, ngel Plaza |
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| Affiliation: | aDepartment of Mathematics, University of Las Palmas de Gran Canaria (ULPGC), 35017-Las Palmas de Gran Canaria, Spain |
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| 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 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. |
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