Results 11 to 20 of about 884 (133)

Generalization of the 2-Fibonacci sequences and their Binet formula [PDF]

Notes on Number Theory and Discrete Mathematics
We will explore the generalization of the four different 2-Fibonacci sequences defined by Atanassov. In particular, we will define recurrence relations to generate each part of a 2-Fibonacci sequence, discuss the generating function and Binet formula of ...
Timmy Ma, Richard Vernon, Gurdial Arora
doaj   +1 more source

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.
Jafari Petroudi SH, Pirouz M, Karaca E, Yılmaz F.   +3 more
europepmc   +2 more sources

On Generalized Tribonacci Octonions

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019
In this paper, we introduced generalized tribonacci octonion sequence which is a generalization of third order recurrence relations. We investigate many identities which are created by using generalized tribonacci sequence.
Arzu Özkoç Öztürk
doaj   +1 more source

The mathematics of generalized Fibonacci sequences: Binet's formula and identities [PDF]

Mathematica Moravica
This article considers a generalized Fibonacci sequence {Vn} with general initial conditions, V0 = a, V1 = b, and a versatile recurrence relation Vn = pVn-1 + qVn-2, where n ≥ 2 and a, b, p and q are any non-zero real numbers. The generating function and
Verma K.L.
doaj   +1 more source

On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers

Axioms, 2023
Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems.
Elen Viviani Pereira Spreafico, Paula Catarino, Paulo Vasco   +2 more
doaj   +1 more source

The Horadam Hybrid Numbers

Discussiones Mathematicae - General Algebra and Applications, 2018
In this paper we introduce the Horadam hybrid numbers and give some their properties: Binet formula, character and generating function.
Szynal-Liana Anetta
doaj   +1 more source

The Representation, Generalized Binet Formula and Sums of The Generalized Jacobsthal p-Sequence

Hittite Journal of Science and Engineering, 2016
In this study, a new generalization of the usual Jacobsthal sequence is presented, which is called the generalized Jacobsthal Binet formula, the generating functions and the combinatorial representations of the generalized Jacobsthal p-sequence are ...
Ahmet Daşdemir
doaj   +1 more source

On the Bicomplex Generalized Tribonacci Quaternions

Mathematics, 2019
In this paper, we introduce the bicomplex generalized tribonacci quaternions. Furthermore, Binet’s formula, generating functions, and the summation formula for this type of quaternion are given. Lastly, as an application, we present the determinant
Can Kızılateş, Paula Catarino, Naim Tuğlu   +2 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

Optical properties of null geodesics emerging from dynamical systems

European Physical Journal C: Particles and Fields, 2022
We study optical metrics via null geodesics as a central force system, deduce the related Binet equation and apply the analysis to certain solutions of Einstein’s equations with and without spherical symmetry.
D. Batic, S. Chanda, P. Guha
doaj   +1 more source