A Note On The Generalized k-Fibonacci Sequence

Year 2021, Volume: 2 Issue: 2, 29 - 39, 18.12.2021

Yashwant Panwar

https://doi.org/10.46572/naturengs.937010

Cited By: 7

Abstract

In this paper, we present a generalization of well-known k-Fibonacci sequence. Namely, we defined generalized k-Fibonacci sequence. This sequence generalizes others, k-Fibonacci sequence, classical Fibonacci sequence, Pell sequence and Jacobsthal sequence. We establish some of the interesting properties of generalized k-Fibonacci sequence. Also, we obtain a generating function for them.

Keywords

Generalized k-Fibonacci sequence, k-Fibonacci sequence, Fibonacci sequence, Binet’s formula, Generating function

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