Results 81 to 90 of about 1,467 (207)

Mersenne-Horadam identities using generating functions

Karpatsʹkì Matematičnì Publìkacìï, 2020
The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
doaj   +1 more source

Subordination Properties of Bi‐Univalent Functions Involving Horadam Polynomials

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this research, we investigate a family of q‐extensions defined on an open unit disk, which is based on bi‐univalent functions associated with differential subordination. Next, we define certain classes of bi‐univalent functions using generalized Horadam polynomials.
Ebrahim Amini, Shrideh Al-Omari, Abdul Rauf Khan   +2 more
wiley   +1 more source

Convoluted convolved Fibonacci numbers

, 2020
The convolved Fibonacci numbers F (r) In this note we consider some related numbers that can be expressed in terms of convolved Fibonacci numbers. These numbers appear in the numerical evaluation of a constant arising in the study of the average density ...
Numbers Fibonacci, Pieter Moree, Convolved Convoluted, P Moree   +3 more
core  

Circulants and the factorization of the Fibonacci–like numbers [PDF]

, 2006
summary:Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev ...
Trojovský, Pavel, Seibert, Jaroslav
core   +1 more source

Bi‐Starlike Function of Complex Order Involving Rabotnov Function Associated With Telephone Numbers

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Telephone numbers defined through the recurrence relation Qn=Qn−1+n−1Qn−2 for n ≥ 2, with initial values of Q0=Q1=1. The study of such numbers has led to the establishment of various classes of analytic functions associated with them. In this paper, we establish two new subclasses of bi‐convex and bi‐starlike functions of complex order in the open unit
Sa’ud Al-Sa’di, Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Ming-Sheng Liu   +3 more
wiley   +1 more source

On the Existence of Solutions of Diophantine Equations Related to Subbalancing Numbers

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, we introduce a new sequence of subbalancing numbers by considering balancing numbers as the values of D in the Diophantine equations provided by subbalancing numbers. For this, first we prove that when the values of the positive integer D are chosen as balancing numbers, there exist integer solutions of the Diophantine equations that ...
Selin Sarı, Gül Karadeniz-Gözeri, Pramita Mishra   +2 more
wiley   +1 more source

A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
wiley   +1 more source

Sums of certain products of fibonacci & Lucas numbers-part III [PDF]

, 2017
For the Fibonacci numbers, the summation formula σnk=1 Fk2=FnFn+1is well-known. Its charm lies in the fact that the right side is a product of terms from the Fibonacci sequence.
Melham, RS
core  

Provando o Compêndio de Hoggatt das Identidades de Fibonacci e Lucas

CQD Revista Eletrônica Paulista de Matemática
Este trabalho tem como objetivo apresentar demonstrações completas para as identidades envolvendo as sequências de Fibonacci e de Lucas listadas por Hoggatt no capítulo 10 de Fibonacci and Lucas Numbers.
Danilo Braga Lopes, Arthur Martins, Lucas Antonio Caritá   +2 more
doaj   +1 more source

On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]

Notes on Number Theory and Discrete Mathematics
Using a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $binom{3n}{n}$ derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established ...
Kunle Adegoke, Robert Frontczak, Taras Goy   +2 more
doaj   +1 more source