Version 1
: Received: 22 April 2020 / Approved: 24 April 2020 / Online: 24 April 2020 (10:35:07 CEST)
How to cite:
Soykan, Y. A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3} $. Preprints2020, 2020040437. https://doi.org/10.20944/preprints202004.0437.v1
Soykan, Y. A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3} $. Preprints 2020, 2020040437. https://doi.org/10.20944/preprints202004.0437.v1
Soykan, Y. A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3} $. Preprints2020, 2020040437. https://doi.org/10.20944/preprints202004.0437.v1
APA Style
Soykan, Y. (2020). A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3} $. Preprints. https://doi.org/10.20944/preprints202004.0437.v1
Chicago/Turabian Style
Soykan, Y. 2020 "A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3} $" Preprints. https://doi.org/10.20944/preprints202004.0437.v1
Abstract
In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3}$ for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.
Keywords
Fibonacci numbers; Lucas numbers; Pell numbers; Jacobsthal numbers; sum formulas
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
