A Note on Golden RATIO and Higher Order Fibonacci Sequences

Paolo Emilio Ricci

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A Note on Golden RATIO and Higher Order Fibonacci Sequences

机译：关于黄金比率和高阶斐波那契数列的注记

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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.

机译：从关于矩阵幂的一般结果开始，得出用费波纳契数表示黄金比例的整数幂的卢卡斯公式。将相同的技术应用于Tribonacci序列，并考虑扩展到更高阶的Fibonacci序列。结果表明，利用矩阵理论的经典结果，可以用一般统一的方法来解决该问题。

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《Turkish Journal of Analysis and Number Theory》 |2020年第1期|共5页
作者
Paolo Emilio Ricci;
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中图分类数学;
关键词
golden ratioFibonacci sequenceTribonacci numbersmatrix theory;

机译：黄金比率斐波那契数列Tribonacci数矩阵理论;

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1. BEATTY SEQUENCES, FIBONACCI NUMBERS,AND THE GOLDEN RATIO [J] . VINCENT RUSSO, LOREN SCHWIEBERT The Fibonacci quarterly . 2011,第2期

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2. From Fibonacci Numbers to Geometric Sequences and the Binet Formula by Way of the Golden Ratio! [J] . Angelo S. DiDomenico Mathematics Teacher . 1997,第5期

机译：从黄金斐波那契数到几何序列和Binet公式！
3. Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s——Part I. Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci Goniometry [J] . Alexey Stakhov, Samuil Aranson Applied Mathematics . 2011,第1期

机译：双曲线斐波那契和卢卡斯函数，“黄金”斐波那契测角法，博德纳几何和希尔伯特的-第一部分。双曲线斐波那契和卢卡斯函数与“金”斐波那契测角法
4. An investigation of application of the golden ratio and Fibonacci sequence in fashion design and pattern making [C] . Z I Kazlacheva World Textile Conference . 2017

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5. Fibonacci sequences and the golden section. [D] . Bodas, Medha A. 2001

机译：斐波那契数列和黄金分割。
6. Researches on Mathematical Relationship of Five Elements of Containing Notes and Fibonacci Sequence Modulo 5 [O] . Zhaoxue Chen 2015

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7. Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s——Part I. Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci Goniometry [O] . Alexey Stakhov, Samuil Aranson 2011

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A Note on Golden RATIO and Higher Order Fibonacci Sequences

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