Some generalized results related to Fibonacci sequence

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-4269

Keywords:

Fibonacci sequence, Cassini’s identity

Abstract

Cassini's identity states that for the nth Fibonacci number Fn+1Fn-1-Fn2=(-1)n, We generalize Fibonacci sequence in terms of the number of sequences. Fibonacci sequence is the particular case of generating only one sequence. This generalization is used to generalize Cassini’s identity. Moreover we prove few more results which can be seen as  generalized form of the results which hold for Fibonacci sequence.

Author Biographies

Neeraj Kumar Paul, Gauhati University.

Dept. of Mathematics.

Helen K. Saikia, Gauhati University,

Dept. of Mathematics

References

N. K. Paul and H. K. Saikia, “A generalization of Fibonacci sequence”, Proyecciones (Antofagasta, on line), vol. 39, no. 6, pp. 1393-1405, 2020, doi: 10.22199/issn.0717-6279-2020-06-0085

D. M. Burton, Elementary number theory, 7th ed. Boston, MA: McGraw-Hill, 2011.

G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 6th ed. Oxford: Oxford University Press, 2008.

N. J. A. Sloane, “A000045:Fibonacci numbers: F(n) = F(n-1) F(n-2) with F(0) = 0 and F(1) = 1.”, The on-line encyclopedia of integer sequences. The OEIS Foundation , 2011 [Online]. Available: https://oeis.org/A000045

Published

2021-04-27

How to Cite

[1]
N. K. Paul and H. K. Saikia, “Some generalized results related to Fibonacci sequence”, Proyecciones (Antofagasta, On line), vol. 40, no. 3, pp. 605-617, Apr. 2021.

Issue

Vol. 40 No. 3 (2021)

Section

Artículos

Copyright (c) 2021 Neeraj Kumar Paul, Helen K. Saikia

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.