General Mathematics

    

Fibonacci Sequence, Golden Ratio and Generalized Additive Sequences

Authors: Asutosh Kumar

In this article, we recall the Fibonacci sequence, the golden ratio, their properties and applications, and some early generalizations of the golden ratio. The Fibonacci sequence is a 2-sequence because it is generated by the sum of two previous terms. As a natural extension of this, we introduce several typical p-sequences where every term is the sum of p-previous terms given p initial values called seeds. In particular, we introduce the notion of 1-sequence. We then discuss generating functions and limiting ratio values of p-sequences. Furthermore, inspired by Fibonacci's rabbit pair problem, we consider a general problem whose particular cases lead to nontrivial additive sequences.

Comments: 28 Pages. 2 figures, 13 tables

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Submission history

[v1] 2021-09-25 03:11:31

Unique-IP document downloads: 1614 times

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