Alternating generalized Fibonacci sequences

Carlos M. da Fonseca and Paulo Saraiva
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 4, Pages 829–838
DOI: 10.7546/nntdm.2025.31.4.829-838
Full paper (PDF, 200 Kb)

Details

Authors and affiliations

Carlos M. da Fonseca
¹ Kuwait College of Science and Technology
² Faculty of Applied Mathematics and Informatics, Technical University of Sofia
Kliment Ohridski Blvd. 8, 1000 Sofia, Bulgaria
³ Chair of Computational Mathematics, University of Deusto
48007 Bilbao, Spain

Paulo Saraiva
⁴ Faculty of Economics, University of Coimbra
Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal
⁵ Centre for Mathematics of the University of Coimbra
Department of Mathematics, University of Coimbra, 3000-143 Coimbra, Portugal
⁶ CeBER – Centre for Business and Economics Research
Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal

Abstract

In a recent paper, K. T. Atanassov and A. G. Shannon introduced a Fibonacci-like sequence derived from the generalized Fibonacci sequence by incorporating alternating signs into the recurrence relation. They also proposed explicit formulas for this sequence. In this work, we present the generating function for the sequence using a matrix-based approach. Furthermore, we explore additional variations of the original definition.

Keywords

• Fibonacci numbers
• Generating function

2020 Mathematics Subject Classification

• 11B39

References

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Manuscript history

• Received: 15 September 2025
• Revised: 29 October 2025
• Accepted: 6 November 2025
• Online First: 12 November 2025

Copyright information

Ⓒ 2025 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).