Results 11 to 20 of about 2,031,724 (254)

On the Leonardo Sequence via Pascal-Type Triangles

Journal of Mathematics
In this study, we discussed the Leonardo number sequence, which has been studied recently and caught more attention. We used Pascal and Hosoya-like triangles to make it easier to examine the basic properties of these numbers.
Serpil Halıcı, Sule Curuk
doaj   +4 more sources

On the Leonardo quaternions sequence [PDF]

Hacettepe Journal of Mathematics and Statistics
In the present work, a new sequence of quaternions related to the Leonardo numbers -- named the Leonardo quaternions sequence -- is defined and studied. Binet's formula and certain sum and binomial-sum identities, some of which derived from the mentioned formula, are established.
Patrícia Beites, Paula Maria Machado Cruz Catarino   +1 more
openaire   +3 more sources

INVESTIGATING THE DUAL QUATERNION EXTENSION OF THE DGC LEONARDO SEQUENCE

In this study, we introduce a new generalization of the Leonardo sequence, dual quaternions with the DGC Leonardo sequence coefficients, depending on the parameter p is an element of R. This generalization gives dual quaternions with the dual-complex Leonardo sequence for p = -1, dual quaternions with the hyper-dual Leonardo sequence for p = 0, and ...
Yilmaz, Cigdemigdem zeynep, Sacli, Gulsum yeliz   +1 more
core   +6 more sources

A Note on Hyper-Dual Numbers With the Leonardo-Alwyn Sequence

Turkish Journal of Mathematics & Computer Science
We are interested in identifying hyper-dual numbers with the Leonardo-Alwyn sequence components. We investigate their homogeneous and non-homogeneous recurrence relations, the Binet’s formula, and the generating function. With these algebraic properties, we are able to obtain some special cases of hyper-dual numbers with the Leonardo-Alwyn sequence ...
Salim Yüce, GÜlsÜm Yelİz ŞentÜrk
exaly   +4 more sources

The Generating Function of a Bi-Periodic Leonardo Sequence

Armenian Journal of Mathematics
In ``"A note on bi-periodic Leonardo sequence", the generating function for a certain bi-periodic Leonardo sequence is claimed.  In this note, we show that the result is not correct. Based on the literature, we establish the correct identity. Possible periodic extensions for the Leonardo sequence are discussed, opening new avenues for results in the ...
exaly   +2 more sources

Explicit Formulas for Polynomial-Type Particular Solutions of Generalized Leonardo-Type Sequences

Asian Journal of Advanced Research and Reports
Recurrence relations provide a powerful framework for understanding numerical sequences, with applications spanning both classical and modern mathematics. In earlier work, explicit iterative formulas for polynomial-type particular solutions of generalized Leonardo-type sequences were derived.
Yuksel Soykan
exaly   +3 more sources

Notes on generalized and extended Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences.
Anthony G. Shannon, Peter J.-S. Shiue, Shen C. Huang   +2 more
doaj   +1 more source

A New Approach to Leonardo Number Sequences With the Dual Vector and Dual Angle Representation

AIMS Mathematics
<abstract><p>In this paper, we introduce dual numbers with components including Leonardo number sequences. This novel approach facilitates our understanding of dual numbers and properties of Leonardo sequences. We also investigate fundamental properties and identities associated with Leonardo number sequences, such as Binet's formula and ...
Babadağ, Faik, Atasoy, Ali
exaly   +3 more sources

A note on generalized and extended Leonardo sequences [PDF]

Notes on Number Theory and Discrete Mathematics, 2022
This note considers some real and complex extensions and generalizations of the Leonardo sequence, which is embedded within each of these two types of intriguing sequences, intriguing because there are still some unanswered questions. The connections between inhomogeneous and homogeneous forms are used as examples of a possible reason that the Leonardo
Anthony G. Shannon, Ömür Deveci
openaire   +1 more source

On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions

Journal of New Theory, 2023
In this paper, we present a new definition, referred to as the Francois sequence, related to the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo and hyperbolic Francois quaternions.
Paula Maria Machado Cruz Catarino, Orhan Dışkaya, Hamza Menken   +2 more
doaj   +1 more source