The k-Fibonacci sequence and the Pascal 2-triangle

By Sergio Falcón, Ángel Plaza. 2007

263 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6f76e94e046fe54c33fb1e74be455198a73a832a

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In Algebra and Number Theory

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

A New Generalization of Fibonacci Sequence & Extended Binet's Formula (2009, background): “Some authors ([13, 15, 17, 27, 37]) have generalized the Fibonacci sequence by preserving the recurrence relation and altering the first two terms of the sequence, while others ([7, 20, 21, 22, 26, 30, 40]) have generalized the Fibonacci sequence by preserving the first two terms of the sequence but”
On the 3-dimensional k-Fibonacci spirals (2008, background): “[16,19] The quasi-sine k-Fibonacci function is defined by FFkðxÞ 1⁄4 rx cosðpxÞr x rþ r 1 where r is the positive characteristic root.”
Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions (2015, background): “Some of the properties that the k-Fibonacci numbers verify are summarized bellow (see [6, 7] for the proofs).”
On k-Fibonacci sequences and polynomials and their derivatives (2009, background): “On the other hand in [21] the k-Fibonacci numbers were given in an explicit way and, by easy arguments, many properties were proven.”
On generalized Fibonacci and Lucas polynomials (2009, background): “On the other hand, in [12] the k-Fibonacci numbers were given in an explicit way and many properties were proven.”
On the k-Lucas Numbers (2011, background): “In [4], we have proved Fk,2n = 1 k (F 2 k,n+1 − F 2 k,n).”
The k-Fibonacci hyperbolic functions (2008, methodology): “There are several identities for these quasi-sine k-Fibonacci functions which are versions of analogous identities of the k-Fibonacci numbers [19,21,23,25, 26 ].”