Relationships between Some *k* -Fibonacci Sequences

Affiliation(s)

Department of Mathematics, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain.

Department of Mathematics, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain.

ABSTRACT

In this paper, we will see that some*k *-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 .

In this paper, we will see that some

Cite this paper

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

Falcon, S. (2014) Relationships between Some

References

[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.

http://members.tripod.com/vismath/

[4] Sloane, N.J.A. The Online Encyclopedia of Integer Sequences. http://oeis.org

[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.

[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.

http://members.tripod.com/vismath/

[4] Sloane, N.J.A. The Online Encyclopedia of Integer Sequences. http://oeis.org

[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.