Research ArticleOpen AccessGoogle Scholar indexed
Relationships between Some <i>k</i> -Fibonacci Sequences
Department of Mathematics, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain
- 1 Department of Mathematics, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain
Applied Mathematics·Volume 05 (2014)·Pages 2226–2234·Published 5 August 2014·DOI10.4236/am.2014.515216
Copy link · social · email
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 .
KeywordsFibonacci and Lucas Numbers<i>k</i>-Fibonacci NumbersPascal Triangle
- Falcon, S. and Plaza, A. (2007) On the Fibonacci k-Numbers. Chaos, Solitons Fractals, 32, 1615-1624.
- Falcon, S. and Plaza, A. (2007) Thek-Fibonacci Sequence and the Pascal 2-Triangle. Chaos, Solitons Fractals, 33, 38-49.
- Spinadel, V.W. (1999) The family of Metallic Means. Vis Math, 1. http://members.tripod.com/vismath/
- Sloane, N.J.A. The Online Encyclopedia of Integer Sequences. http://oeis.org
- Falcon, S. and Diaz-Barreiro, J.L. (2006) Some Properties of Sums Involving Pell Numbers. Missouri Journal of Mathematical of Sciences, 18, 33-40.