Results 11 to 20 of about 894 (158)

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

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

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

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

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

Dual Leonardo numbers

AIMS Mathematics, 2023
This paper introduced the concept of dual Leonardo numbers to generalize the earlier studies in harmony and establish key formulas, including the Binet formula and the generating function. Both were employed to obtain specific elements from the sequence.
Adnan Karataş
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

A Context-Free Grammar Associated with Fibonacci and Lucas Sequences

Journal of Mathematics, 2023
We introduce a context-free grammar G=s⟶s+d,d⟶s to generate Fibonacci and Lucas sequences. By applying the grammar G, we give a grammatical proof of the Binet formula.
Harold Ruilong Yang
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

Binomial transform of the bivariate Fibonacci quaternion polynomials and its properties [PDF]

Notes on Number Theory and Discrete Mathematics
The primary aim of this work is to deal with binomial transforms of bivariate Fibonacci quaternion polynomial sequence. The binomial sequence of the bivariate Fibonacci quaternion polynomial is found, and then results are obtained for the recurrence ...
Faruk Kaplan, Arzu Özkoç Öztürk
doaj   +1 more source