Two 2-Fibonacci sequences generated by a mixed scheme. Part 1

Krassimir T. Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 2, Pages 331–338
DOI: 10.7546/nntdm.2022.28.2.331-338
Full paper (PDF, 227 Kb)

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Authors and affiliations

Krassimir T. Atanassov
Department of Bioinformatics and Mathematical Modelling,
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
Acad. G. Bonchev Str. Bl. 105, Sofia-1113, Bulgaria

Abstract

A new scheme of 2-Fibonacci sequences is introduced and the explicit formulas for its n-th members are given. For difference of all previous sequences from Fibonacci type, the present 2-Fibonacci sequences are obtained by a new way. It is proved that the new sequences have bases with 48 elements about function 𝜑 and modulo 9.

Keywords

• Fibonacci sequence
• 2-Fibonacci sequence

2020 Mathematics Subject Classification

• 11B39

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Manuscript history

• Received: 12 March 2022
• Revised: 11 May 2022
• Accepted: 11 May 2022
• Online First: 12 May 2022