Fibonacci and lucas sequences - Open Access .click

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Analytical Characterization of Self-Similarity in k-Cullen Sequences Through Generating Functions and Fibonacci Scaling

Fractal and Fractional
In this study, we define the k-Cullen, k-Cullen–Lucas, and Modified k-Cullen sequences, and certain terms in these sequences are given. Then, we obtain the Binet formulas, generating functions, summation formulas, etc.
Hakan Akkuş, Bahar Kuloğlu, Engin Özkan +2 more
doaj +1 more source

A note on the bi-periodic Fibonacci and Lucas matrix sequences

, 2016
In this paper, we introduce the bi-periodic Lucas matrix sequence and present some fundamental properties of this generalized matrix sequence. Moreover, we investigate the important relationships between the bi-periodic Fibonacci and Lucas matrix sequences. We express that some behaviours of bi-periodic Lucas numbers also can be obtained by considering
Coskun, Arzu, Yilmaz, Nazmiye, Taskara, Necati +2 more
openaire +2 more sources

Global Behavior of Solutions to a Higher-Dimensional System of Difference Equations with Lucas Numbers Coefficients

Mathematical and Computational Applications
In this paper, we derive the well-defined solutions to a θ-dimensional system of difference equations. We show that, the well-defined solutions to that system are represented in terms of Fibonacci and Lucas sequences.
Messaoud Berkal +2 more
doaj +1 more source

On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. [PDF]