Relationships between Some k -Fibonacci Sequences


In this paper, we will see that some -Fibonacci sequences are related to the classical Fibonacci sequence of such way that we can express the terms of a k -Fibonacci sequence in function of some terms of the classical Fibonacci sequence. And the formulas will apply to any sequence of a certain set of k' -Fibonacci sequences. Thus we find k -Fibonacci sequences relating to other k -Fibonacci sequences when σ'k is linearly dependent of .

Share and Cite:

Falcon, S. (2014) Relationships between Some k -Fibonacci Sequences. Applied Mathematics, 5, 2226-2234. doi: 10.4236/am.2014.515216.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Falcon, S. and Plaza, A. (2007) On the Fibonacci k-Numbers. Chaos, Solitons Fractals, 32, 1615-1624.
[2] Falcon, S. and Plaza, A. (2007) Thek-Fibonacci Sequence and the Pascal 2-Triangle. Chaos, Solitons Fractals, 33, 38-49.
[3] Spinadel, V.W. (1999) The family of Metallic Means. Vis Math, 1.
[4] Sloane, N.J.A. The Online Encyclopedia of Integer Sequences.
[5] Falcon, S. and Diaz-Barreiro, J.L. (2006) Some Properties of Sums Involving Pell Numbers. Missouri Journal of Mathematical of Sciences, 18, 33-40.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.