Results 31 to 40 of about 13,753 (265)

A note on a bivariate Leonardo sequence [PDF]

Notes on Number Theory and Discrete Mathematics
Recently, quite a few generalizations of Leonardo numbers have emerged in the literature. In this short note, we propose a new bivariate extension and provide its generating function.
Carlos M. da Fonseca, Anthony G. Shannon
doaj   +2 more sources

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   +2 more sources

Determinants of Toeplitz–Hessenberg Matrices with Generalized Leonardo Number Entries

Annales Mathematicae Silesianae
Let un = un(k) denote the generalized Leonardo number defined recursively by un = un−1 + un−2 + k for n ≥ 2, where u0 = u1 = 1. Terms of the sequence un(1) are referred to simply as Leonardo numbers.
Goy Taras, Shattuck Mark
doaj   +2 more sources

On Leonardo p-numbers

, 2023
In this paper, we introduce a new generalization of Leonardo numbers, which are so-called Leonardo $p$-numbers. We investigate some basic properties of these numbers. We also define incomplete Leonardo $p$-numbers which generalize the incomplete Leonardo numbers.
Tan, Elif, Leung, Ho-Hun
openaire   +2 more sources

Bivariate Leonardo polynomials and Riordan arrays [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, bivariate Leonardo polynomials are defined, which are closely related to bivariate Fibonacci polynomials. Bivariate Leonardo polynomials are generalizations of the Leonardo polynomials and Leonardo numbers.
Yasemin Alp, E. Gökçen Koçer
doaj   +1 more source

A Note on Incomplete Leonardo Numbers

, 2020
See the abstract in the attached pdf.
Catarino, P., Borges, A.
openaire   +2 more sources

A K3 surface related to Leonardo Pisano’s work on congruent numbers [PDF]

, 2023
This note recalls an early 13th century result on congruent numbers by Leonardo Pisano (“Fibonacci”), and shows how it relates to a specific much studied K3 surface and to an elliptic fibration on this surface.
Top, Jaap, Top, Jaap; id_orcid, Jaap Top, Djukanović, Martin, Martin Djukanović   +4 more
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Dynamical analysis of the M-ℂomplex Lorenz system and its anti-synchronization via M-Sliding mode control

Results in Physics, 2022
This work deals with a numerical analysis of a Complex Lorenz system generalized by the truncated M-derivative (M-ℂLM). First, we carry out 10000 random simulations based on the Monte Carlo principle and the 0–1 test with the chaos decision tree to show ...
J.E. Solís-Pérez, J.F. Gómez-Aguilar, J.A. Hernández-Pérez, J. Torres-Jiménez   +3 more
doaj   +1 more source

Non-Fisherian generalized Fibonacci numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Using biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
doaj   +1 more source

Generalized Leonardo Numbers

, 2021
In this paper, we investigate the generalized Leonardo sequences and we deal with, in detail, three special cases, namely, modified Leonardo, Leonardo-Lucas and Leonardo sequences.
Soykan, Yüksel
core