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Ordered Leonardo Quadruple Numbers

Symmetry, 2023
In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric properties of Fibonacci numbers are used in the proofs.
Semra Kaya Nurkan
exaly   +4 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   +2 more sources

Construction of generalized bicomplex Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we introduce a new class of bicomplex numbers whose components are expressed in terms of bicomplex Leonardo numbers. The motivation for this study arises from the growing interest in generalizations of well-known integer sequences within ...
Murat Turan, Sıddıka Özkaldı Karakuş   +1 more
doaj   +2 more sources

Special Cases of Generalized Leonardo Numbers : Modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo Numbers

Earthline Journal of Mathematical Sciences, 2022
In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences.
Yüksel Soykan
openaire   +3 more sources

Pell Leonardo numbers and their matrix representations

Journal of New Results in Science
In this study, we investigate Pell numbers and Leonardo numbers and describe a new third-order number sequence entitled Pell Leonardo numbers. We then construct some identities, including the Binet formula, generating function, exponential generating ...
Çağla Çelemoğlu
doaj   +3 more sources

On the Generalized Leonardo Numbers

, 2022
See the abstract in the attached pdf.
Kuhapatanakul, Kantaphon, Chobsorn, Juthamas   +1 more
openaire   +3 more sources

Leonardo da Vinci’s Contributions from a Design Perspective

Designs, 2020
The figure of Leonardo da Vinci has been extensively studied. In fact, the Leonardiana Library brings together tens of thousands of titles on Leonardo and his work.
Ernesto Cerveró-Meliá, Salvador F. Capuz-Rizo, Pablo Ferrer-Gisbert   +2 more
doaj   +1 more source

GAUSSIAN LEONARDO POLYNOMIALS AND APPLICATIONS OF LEONARDO NUMBERS TO CODING THEORY

Journal of Science and Arts, 2023
In this paper, we firstly introduce the Gaussian Leonardo polynomial sequences {GLe_n (x)}_(n=0)^∞ and we obtain Binet's formula, generating function of this sequence. Moreover, we define the matrix Gl(x) in the form of 3 x 3. Finally, we study on the coding and decoding applications of the Leonardo number by using the Leonardo matrix P.
SELİME BEYZA ÖZÇEVİK, ABDULLAH DERTLİ   +1 more
openaire   +1 more source

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

Generalized Bronze Leonardo sequence [PDF]

Notes on Number Theory and Discrete Mathematics
In this study, we define the Bronze Leonardo, Bronze Leonardo–Lucas, and Modified Bronze Leonardo sequences, and some terms of these sequences are given. Then, we give special summation formulas, special generating functions, etc.
Engin Özkan, Hakan Akkuş
doaj   +1 more source