Results 1 to 10 of about 536 (105)

A combined approach to Perrin and Padovan hybrid sequences [PDF]

Heliyon, 2021
Recently, there has been huge interest to a new numeric set, which brings together three numerical systems: complex, hyperbolic and dual numbers, called as hybrid number.
Seyyed H. Jafari Petroudi, Maryam Pirouz, Emel Karaca, Fatih Yılmaz   +3 more
doaj   +2 more sources

Some geometric properties of the Padovan vectors in Euclidean 3-space [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
Padovan numbers were defined by Stewart (1996) in honor of the modern architect Richard Padovan (1935) and were first discovered in 1924 by Gerard Cordonnier.
Serdar Korkmaz, Hatice Kuşak Samancı
doaj   +1 more source

On the bi-periodic Padovan sequences [PDF]

Mathematica Moravica, 2023
In this study, we define a new generalization of the Padovan numbers, which shall also be called the bi-periodic Padovan sequence. Also, we consider a generalized bi-periodic Padovan matrix sequence. Finally, we investigate the Binet formulas, generating
Dışkaya Orhan, Menken Hamza
doaj   +1 more source

On the bivariate Padovan polynomials matrix [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this paper, we intruduce the bivariate Padovan sequence we examine its various identities. We define the bivariate Padovan polynomials matrix. Then, we find the Binet formula, generating function and exponential generating function of the bivariate ...
Orhan Dişkaya, Hamza Menken, Paula Maria Machado Cruz Catarino   +2 more
doaj   +1 more source

On Dual Quaternions with $k-$Generalized Leonardo Components

Journal of New Theory, 2023
In this paper, we define a one-parameter generalization of Leonardo dual quaternions, namely $k-$generalized Leonardo-like dual quaternions. We introduce the properties of $k$-generalized Leonardo-like dual quaternions, including relations with Leonardo,
Gülsüm Yeliz Saçlı, Çiğdem Zeynep Yılmaz   +1 more
doaj   +1 more source

The sequence of trifurcating Fibonacci numbers

Ratio Mathematica, 2021
One of the interesting generalizations of Fibonacci sequence is a k-Fibonacci sequence, which is further generalized into the ‘Bifurcating Fibonacci sequence’.
Parimalkumar A. Patel, Dr. Devbhadra V. Shah   +1 more
doaj   +1 more source

On the Richard and Raoul numbers

Journal of New Results in Science, 2022
In this study, we define and examine the Richard and Raoul sequences and we deal with, in detail, two special cases, namely, Richard and Raoul sequences. We indicate that there are close relations between Richard and Raoul numbers and Padovan and Perrin
Orhan Dışkaya, Hamza Menken
doaj   +1 more source

On a generalization of the Gadovan numbers [PDF]

Mathematica Moravica
In this paper, we define (k, l)-Gadovan numbers. We give the Binet-like formula, the generating functions, the exponential generating function of the (k, l)-Gadovan numbers. Also, we derive Cassinilike identity, Catalan-like identity, Vajda-like identity,
Özkan Engın, Eser Engın, Uysal Mıne
doaj   +1 more source

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   +1 more source

Horadam Octonions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
In this paper, first we define Horadam octonions by Horadam sequence which is a generalization of second order recurrence relations. Also, we give some fundamental properties involving the elements of that sequence.
Karataş Adnan, Halici Serpil
doaj   +1 more source