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R. Lidl, C. Wells, Chebyshev polynomials in several variables, J. Reine Angew. Math., 255, (1972), 104-111.

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Article

A Note on Golden Ratio and Higher Order Fibonacci Sequences

1Mathematics Department, International Telematic University UniNettuno, Roma, Italia


Turkish Journal of Analysis and Number Theory. 2020, Vol. 8 No. 1, 1-5
DOI: 10.12691/tjant-8-1-1
Copyright © 2020 Science and Education Publishing

Cite this paper:
Paolo Emilio Ricci. A Note on Golden Ratio and Higher Order Fibonacci Sequences. Turkish Journal of Analysis and Number Theory. 2020; 8(1):1-5. doi: 10.12691/tjant-8-1-1.

Correspondence to: Paolo  Emilio Ricci, Mathematics Department, International Telematic University UniNettuno, Roma, Italia. Email: paoloemilioricci@gmail.com

Abstract

The Lucas formula representing integer powers of the Golden ratio in terms of Fibonacci numbers is derived starting from a general result on matrix powers. The same technique is applied to the Tribonacci sequence, and the extension to higher-order Fibonacci sequences is also considered. It is shown that, by using classical results on matrix theory, the problem can be treated in a general and uniform method.

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