On the Fibonacci k-numbers

By Sergio Falcón, Ángel Plaza. 2007

354 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Materials Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a615c2399741506001ea037a884086cee155e18f

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In Algebra and Number Theory

In Materials Chemistry

In Statistical and Nonlinear Physics

Citations in the corpus

Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions (2015, background): “[5] S. Falcón and A. Plaza, On k-Fibonacci sequences and polynomials and their derivatives, Chaos Solitons Fractals 39(3)(2009), 1005–1019.”
On some identities and generating functions for k- Pell numbers (2013, background): “, in [14], consider some properties for k-Fibonacci numbers obtained from elementary matrix algebra and its identities including generating function and divisibility properties appears in the paper of Bolat et al.”
On Some Identities for k-Fibonacci Sequence (2014, methodology): “[12] S. Falcón, Á. Plaza, “On the Fibonacci k-numbers”, Chaos, Solitons & Fractals, 32(5) (2007), 1615-1624.”
On the m-extension of the Fibonacci and Lucas p-numbers (2009, background): “The Fibonacci m-numbers are same the Fibonacci k-numbers which define in [22,23].”
On generalized Fibonacci and Lucas polynomials (2009, background): “Falcón and Plaza [11] introduced a general Fibonacci sequence that generalizes, among others, both the classical Fibonacci sequence and the Pell sequence.”
On the k-Lucas Numbers (2011, background): “}: A006190 Some of the properties that the k-Fibonacci sequences verify are summarized bellow, (see [3, 4] for details of the proofs):”
On k-Fibonacci sequences and polynomials and their derivatives (2009, background): “Function fkðxÞ 1⁄4 x 1 kx x2 is the generating function of the k-Fibonacci polynomials [20].”
The k-Fibonacci hyperbolic functions (2008, methodology): “rþr� 1 , where r = rk is the positive root of the characteristic equation [ 25 ].”
The k-Fibonacci sequence and the Pascal 2-triangle (2007, background): “In [40] we showed the relation between the 4-triangle longest-edge (4TLE) partition and the Fibonacci numbers, as another example of the relation between geometry and numbers.”
On the 3-dimensional k-Fibonacci spirals (2008, methodology): “For any integer n P 1 holds: ðR 1 LÞ 1⁄4 F k;nþ1 F k;n F k;n F k;nþ1 F k;n 1 F k;n þ F k;n 1 In [14], the following properties are proven.”