Results 21 to 30 of about 973 (216)

On the k-generalized Fibonacci numbers

, 2012
In this paper, we define a new family of k-generalized Fibonacci numbers. Furthermore, we give sums and recurrence relations of this numbers and obtain generating functions of this numbers for k=2.
Yılmaz, Nazmiye, Yazlık, Yasin, Taşkara, Necati   +2 more
openaire   +2 more sources

Binomial Sum Relations Involving Fibonacci and Lucas Numbers

AppliedMath, 2023
In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different ...
Kunle Adegoke, Robert Frontczak, Taras Goy   +2 more
doaj   +1 more source

Generalized Hybrid Fibonacci and Lucas p-numbers

, 2022
The hybrid numbers are a generalization of complex, hyperbolic and dual numbers. Until this time, many researchers have studied related to hybrid numbers.
Kocer, E. Gokcen, Alsan, Huriye
core   +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

On a generalization of dual-generalized complex Fibonacci quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this study, we introduce a new class of generalized quaternions whose components are dual-generalized complex Horadam numbers. We investigate some algebraic properties of them.
Elif Tan, Umut Öcal
doaj   +1 more source

Square numbers, square pyramidal numbers, and generalized Fibonacci polynomials

Journal of New Results in Science, 2022
In this paper, we derive two interesting formulas for square and square pyramidal numbers. We focus on the linear recurrence relation with constant coefficients for square and square pyramidal numbers.
Adem Şahin
doaj   +1 more source

Generalized Fibonacci Numbers, Cosmological Analogies, and an Invariant [PDF]

Symmetry, 2021
Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing a spatially homogeneous and isotropic cosmology in general relativity. These analogies are presented together with their Lagrangian and Hamiltonian formulations and with an invariant of the Fibonacci sequence.
Valerio Faraoni, Farah Atieh
openaire   +2 more sources

On Fibonacci (k,p)-Numbers and Their Interpretations

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023
In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to
Berke Cengiz, Yasemin Taşyurdu
doaj   +1 more source

Some properties of k-generalized fibonacci numbers

, 2021
In the present paper, we propose some properties of the new family K-generalized Fibonacci numbers which related to generalized Fibonacci numbers. Moreover, we give some identities involving binomial coefficients for K-generalized Fibonacci numbers ...
Aydoğdu, A., Özkan, E., Yılmaz, N.
core   +1 more source

On Divisibility of Generalized Fibonacci Numbers

Integers, 2015
See the abstract in the attached pdf.
Miho Aoki, Yuho Sakai
openaire   +4 more sources