Results 121 to 130 of about 187 (159)

On the Binomial Sums of k-Fibonacci and k -Lucas sequences

AIP Conference Proceedings, 2011
The main purpose of this paper is to establish some new properties of k‐Fibonacci and k‐Lucas numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between k‐Fibonacci and k‐Lucas numbers are revealed to get a more strong result.
N. Yilmaz, N. Taskara, K. Uslu, Y. Yazlik, Theodore E. Simos, George Psihoyios, Ch. Tsitouras, Zacharias Anastassi   +7 more
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Gaussian bi-periodic Fibonacci and Gaussian bi-periodic Lucas sequences

Sigmae, 2021
In this study, we bring into light of the gaussian bi-periodic Fibonacci and gaussian bi-periodic Lucas sequences. The Binet formula as well as the generating function for these sequences are given. The convergence property of the consecutive terms of this sequence is examined after which the well known Cassini, Catalan and the D'ocagne identities as ...
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Some identities for generalized Fibonacci and Lucas sequences

2013
In this study, we define a generalization of Lucas sequence {pn}. Then we obtain Binet formula of sequence {pn}. Also, we investigate relationships between generalized Fibonacci and Lucas sequences. © 2013, Hacettepe University. All rights reserved.
IRMAK, Nurettin, ALP, Murat
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First Derivative Sequences of Extended Fibonacci and Lucas Polynomials

1998
In this article we conclude our investigation on the Fibonacci and Lucas derivative sequences by generalizing the sequences \( \left\{ {F\begin{array}{*{20}{c}} {(1)} \\ n \\ \end{array} } \right\} \) and \( \left\{ {L\begin{array}{*{20}{c}} {(1)} \\ n \\ \end{array} } \right\} \) and \( \left\{ {G\begin{array}{*{20}{c}} {(1)} \\ n \\ \end{array ...
Piero Filipponi, Alwyn F. Horadam
openaire   +1 more source

FIBONACCI AND LUCAS SEQUENCES AS THE PRINCIPAL MINORS OF SOME INFINITE MATRICES

Journal of Algebra and Its Applications, 2009
In the literature one may encounter certain infinite tridiagonal matrices, the principal minors of which, constitute the Fibonacci or Lucas sequence. The major purpose of this article is to find new infinite matrices with this property. It is interesting to mention that the matrices found are not tridiagonal which have been investigated before ...
Moghaddamfar, A. R., Pooya, S. M. H., Salehy, S. Navid, Salehy, S. Nima   +3 more
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Some Subsequences of the Generalized Fibonacci and Lucas Sequences

2019
We derive first-order nonlinear homogeneous recurrence relations for certain subsequences of generalized Fibonacci and Lucas sequences. We also present a polynomial representation for the terms of Lucas subsequence.
Kılıç, Emrah, Kılıç, Elif Tan
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New recurrences on Pell numbers, Pell-Lucas numbers, Jacobsthal numbers, and Jacobsthal-Lucas numbers

Chaos, Solitons and Fractals, 2021
Songül Çelik, Engin Özkan
exaly  

Second Derivative Sequences of Fibonacci and Lucas Polynomials

The Fibonacci Quarterly, 1993
Piero Filipponi, Alwyn F. Horadam
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Periodic Fibonacci and Lucas Sequences

The Fibonacci Quarterly, 1991
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The Fibonacci and Lucas Sequences as Structural Codes of DNA

This white paper presents a visionary model linking the Fibonacci and Lucas sequences to the architecture of DNA, codons, amino acids, and chromosomes. Through recursive structures, digital root triplets, and dimensional resonance points, the study reveals deep numerical patterns embedded in biological systems.
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