Next Article in Journal
Symmetric Identities Involving the Extended Degenerate Central Fubini Polynomials Arising from the Fermionic p-Adic Integral on \({\mathbb{Z}_{p}}\)
Next Article in Special Issue
Monogenity and Power Integral Bases: Recent Developments
Previous Article in Journal
Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow
Previous Article in Special Issue
The New G-Double-Laplace Transforms and One-Dimensional Coupled Sine-Gordon Equations
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Generalization of the Distance Fibonacci Sequences

1
Graduate School of Natural and Applied Sciences, Erzincan Binali Yıldırım University, Erzincan 24100, Türkiye
2
Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, 35-959 Rzeszów, Poland
3
Department of Mathematics, Faculty of Science, Marmara University, Istanbul 34722, Türkiye
*
Author to whom correspondence should be addressed.
Submission received: 25 May 2024 / Revised: 13 June 2024 / Accepted: 18 June 2024 / Published: 21 June 2024

Abstract

In this study, we introduced a generalization of distance Fibonacci sequences and investigate some of its basic properties. We then proposed a generalization of distance Fibonacci sequences for negative integers and investigated some basic properties. Additionally, we explored the construction of matrix generators for these sequences and offered a graphical representation to clarify their structure. Furthermore, we demonstrated how these generalizations can be applied to obtain the Padovan and Narayana sequences for specific parameter values.
Keywords: distance Fibonacci numbers; generalized Fibonacci numbers; negative integers; matrix generators distance Fibonacci numbers; generalized Fibonacci numbers; negative integers; matrix generators

Share and Cite

MDPI and ACS Style

Yilmaz, N.Ş.; Włoch, A.; Özkan, E. Generalization of the Distance Fibonacci Sequences. Axioms 2024, 13, 420. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms13070420

AMA Style

Yilmaz NŞ, Włoch A, Özkan E. Generalization of the Distance Fibonacci Sequences. Axioms. 2024; 13(7):420. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms13070420

Chicago/Turabian Style

Yilmaz, Nur Şeyma, Andrej Włoch, and Engin Özkan. 2024. "Generalization of the Distance Fibonacci Sequences" Axioms 13, no. 7: 420. https://0-doi-org.brum.beds.ac.uk/10.3390/axioms13070420

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop