New Number Sequences Obtained with Grouping of Fibonacci Numbers

Authors

  • İnan Durukan Erzincan Binali Yıldırım University
  • Engin Özkan Erzincan Binali Yıldırım University

DOI:

https://doi.org/10.37591/rrdms.v7i3.2594

Keywords:

Binet Formula, Fibonacci sequence, the generalized Fibonacci sequence, Generating functions, Lucas sequence.

Abstract

Abstract

The relations of the sum and difference of two Fibonacci numbers, in which the difference of subscripts is even, was given by Koshy. In this study, the relations of the sum and difference of two Fibonacci numbers, in which is the difference of subscripts is odd, is introduced by using the generating functions. Similar results are given for Lucas numbers. Also, two new family of Fibonacci numbers are obtained.

 

Keywords: Binet Formula, Fibonacci sequence, the generalized Fibonacci sequence, Generating functions, Lucas sequence.

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Published

2021-01-16

Issue

Vol. 7 No. 3 (2020)

Section

Research Articles

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