Results 81 to 90 of about 973 (216)

On the growth rate of generalized Fibonacci numbers

Advances in Difference Equations, 2004
Let α(t) be the limiting ratio of the generalized Fibonacci numbers produced by summing along lines of slope t through the natural arrayal of Pascal's triangle. We prove that is an even function.
Fishkind Donniell E
doaj   +2 more sources

A Pincherle‐Type Convergence Theorem for Generalized Continued Fractions in Banach Algebras

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This contribution is dedicated to the interdependence of higher order linear difference equations and generalized continued fractions in Banach algebras. It turns out that the computation of certain subdominant solutions of a higher order linear difference equation can be done more efficiently by considering its adjoint equation.
Hendrik Baumann, Thomas Hanschke, Arpan Hazra   +2 more
wiley   +1 more source

Some Properties of the Generalized Leonardo Numbers

Journal of New Theory
In this study, various properties of the generalized Leonardo numbers, which are one of the generalizations of Leonardo numbers, have been investigated. Additionally, some identities among the generalized Leonardo numbers have been obtained. Furthermore,
Yasemin Alp
doaj   +1 more source

Determinants Containing Powers of Generalized Fibonacci Numbers

J. Integer Seq., 2015
We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These studies have led us to discover a fundamental identity of determinant involving powers of linear polynomials. Finally,
Aram Tangboonduangjit, Thotsaporn Thanatipanonda   +1 more
openaire   +4 more sources

Leonardo Cartan Numbers and Related Fibonacci–Lucas Structures

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper investigates the Leonardo Cartan numbers, defined as an extension of the classical Leonardo sequence through additional algebraic structures. The recurrence relations of these numbers are established, and various summation formulas are derived.
Hasan Çakır, İskender Öztürk, Smritijit Sen   +2 more
wiley   +1 more source

Matrices of Fibonacci Numbers

, 1981
The matrices of Fibonacci numbers (called windows) possess some unusual properties which are not shared by normal matrices, such as commutativity under multiplication and +1 for all determinants.
M.C. Er
core  

The period of the Fibonacci random number generator

Discrete Applied Mathematics, 1988
The Fibonacci random number generator \(r_ n\equiv r_{n-1}+r_{n- k}(mod M)\) is in focus in this paper. For M prime and some choices of k, any non-zero starting vector \(v=(r_ 1,...,r_ k)\) for integers creates a sequence of maximal period M k-1. In most cases, however, different v's give rise to different periods.
openaire   +1 more source

Split Quaternionic Representations of Horadam Sequences and Their Binet, Generating Function, and Cassini‐Type Identities

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study establishes a novel algebraic connection between Horadam numbers and the split quaternion algebra. To this end, two fundamental constructs are introduced: the Fibonacci Sq,r‐split quaternions and the Horadam sq,r‐split quaternions, which generalize Horadam numbers within the framework of split quaternions.
İskender Öztürk, Hasan Çakır, Smritijit Sen   +2 more
wiley   +1 more source

Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials

, 2002
In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are ...
Qi, Feng, Luo, Qiu-Ming
core  

QUANTUM COIN FLIPPING, QUBIT MEASUREMENT, AND GENERALIZED FIBONACCI NUMBERS

, 2021
The problem of Hadamard quantum coin measurement in n trials, with an arbitrary number of repeated consecutive last states, is formulated in terms of Fibonacci sequences for duplicated states, Tribonacci numbers for triplicated states, and N-Bonacci ...
Pashaev, O. K.
core   +1 more source