A generalization of Fibonacci sequence

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-06-0085

Keywords:

Fibonacci sequence

Abstract

We attempt to generalize Fibonacci sequence by generating certain number of sequences whose terms are obtained by adding the last two generated terms of the preceding sequence. When we consider the particular case of generating only one sequence we obtain the Fibonacci sequence. Moreover we prove some of the results which can be seen as generalized form of the results which hold for Fibonacci sequence. We also verify the results for the particular case of Fibonacci sequence.

Author Biographies

Neeraj Kumar Paul, Gauhati University.

Dept. of Mathematics.

Helen K. Saikia, Gauhati University.

Dept. of Mathematics

References

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,” The On-Line Encyclopedia of Integer Sequences, 26-Oct-2020. [Online]. Available: https://oeis.org/A000045

“Generalizations of Fibonacci numbers”, Wikipedia, 2020. [On line]. Available: https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers

Published

2020-11-12

How to Cite

[1]
N. K. Paul and H. K. Saikia, “A generalization of Fibonacci sequence”, Proyecciones (Antofagasta, On line), vol. 39, no. 6, pp. 1393-1405, Nov. 2020.

Issue

Section

Artículos