Alternating generalized Fibonacci sequences
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.
Authors
- Carlos M. da Fonseca (ORCID: https://orcid.org/0000-0001-7742-4416)
- Paulo Saraiva (ORCID: https://orcid.org/0000-0002-2856-5033)
Publication Details
- Journal
- Notes on Number Theory and Discrete Mathematics
- Published
- 2025-11-12
- DOI
- https://doi.org/10.7546/nntdm.2025.31.4.829-838
- Primary Topic
- Advanced Mathematical Theories and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Universidade de Coimbra
- Ministério da Ciência, Tecnologia e Ensino Superior
- Fundação para a Ciência e a Tecnologia
- Centro de Matemática, Universidade de Coimbra