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On the Fibonacci k-numbers

- S. Falcón, Angel Plaza
- Mathematics
- 1 June 2007

We introduce a general Fibonacci sequence that generalizes, between others, both the classic Fibonacci sequence and the Pell sequence. These general kth Fibonacci numbers {Fk,n}n=0∞ were found by… Expand

231 21

The k-Fibonacci sequence and the Pascal 2-triangle

- S. Falcón, Angel Plaza
- Mathematics
- 1 July 2007

The general k-Fibonacci sequence {Fk,n}n=0∞ were found by studying the recursive application of two geometrical transformations used in the well-known 4-triangle longest-edge (4TLE) partition. This… Expand

171 9- PDF

On the k-Lucas Numbers

- S. Falcón
- Mathematics
- 2011

From a special sequence of squares of k-Fibonacci numbers, the kLucas sequences are obtained in a natural form. Then, we will study the properties of the k-Lucas numbers and will prove these… Expand

79 8- PDF

On k-Fibonacci sequences and polynomials and their derivatives

- S. Falcón, Angel Plaza
- Mathematics
- 15 February 2009

The k-Fibonacci polynomials are the natural extension of the k-Fibonacci numbers and many of their properties admit a straightforward proof. Here in particular, we present the derivatives of these… Expand

92 4- PDF

On k-Fibonacci numbers of arithmetic indexes

- S. Falcón, Angel Plaza
- Mathematics, Computer Science
- Appl. Math. Comput.
- 1 February 2009

TLDR

50 4- PDF

On the complex k-Fibonacci numbers

- S. Falcón
- Mathematics
- 27 July 2016

We first study the relationship between the k-Fibonacci numbers and the elements of a subset of . Later, and since generally studies that are made on the Fibonacci sequences consider that these… Expand

4 2- PDF

Mesh quality improvement and other properties in the four-triangles longest-edge partition

- Angel Plaza, J. P. Suárez, Miguel A. Padrón, S. Falcón, Daniel Amieiro
- Mathematics, Computer Science
- Comput. Aided Geom. Des.
- 1 April 2004

TLDR

31 1

The k–Fibonacci difference sequences

- S. Falcón
- Mathematics
- 1 June 2016

Abstract In this paper we apply the concept of difference relation to the sequences of k –Fibonacci numbers. We will obtain general formulas to find any term of the ith k –Fibonacci difference… Expand

7 1

Binomial Transforms of the k-Fibonacci Sequence

- S. Falcón, Angel Plaza
- Mathematics
- 2009

In this paper, we apply the binomial, k-binomial, rising, and falling transforms to the k-Fibonacci sequence. Many formulas relating the so obtained new sequences are presented and proved. Finally,… Expand

28 1

On the k-Lucas Numbers of Arithmetic Indexes

- S. Falcón
- Mathematics
- 11 October 2012

In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly… Expand

10 1- PDF

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