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Relationships between Some k -Fibonacci Sequences

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DOI: 10.4236/am.2014.515216    4,541 Downloads   5,106 Views  
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ABSTRACT

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 .

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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

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.

  
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