Identities on generalized Fibonacci and Lucas numbers

K. M. Nagaraja and P. Dhanya
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 3, Pages 189–202
DOI: 10.7546/nntdm.2020.26.3.189-202
Full paper (PDF, 205 Kb)

Details

Authors and affiliations

K. M. Nagaraja
Department of Mathematics, J.S.S. Academy of Technical Education
Uttarahalli-Kengeri Main Road, Bengaluru-60, Karnataka, India

P. Dhanya
Department of Mathematics, J.S.S. Academy of Technical Education
Uttarahalli-Kengeri Main Road, Bengaluru-60, Karnataka, India

Abstract

In this article, the concepts of Fibonacci, Tribonacci, Lucas and Tetranacci numbers are generalized as continued sum. The generalized Fibonacci identity is proved by using induction and the binomial theorem. Further, it is proved that the generalized Fibonacci and Lucas sequences are logarithmically convex (concave) and some special identities are obtained.

Keywords

• Sequence
• Fibonacci number
• Lucas number
• Tribonacci number
• Golden ratio

2010 Mathematics Subject Classification

• 11B39

References

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