Results 51 to 60 of about 48,003 (223)

On the sum of the reciprocals of k-generalized Fibonacci numbers

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2022
In this note, we that if { Fn(k) }n≥0 {\left\{ {F_n^{\left( k \right)}} \right\}_{n \ge 0}} denotes the k-generalized Fibonacci sequence then for n ≥ 2 the closest integer to the reciprocal of ∑m≥n1/Fm(k) \sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}}
Adel Alahmadi, F. Luca
semanticscholar   +1 more source

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

Nature-Inspired Design Strategies for Efficient Atmospheric Water Harvesting. [PDF]

Adv Mater
This review presents advances in bioinspired atmospheric water harvesting systems, emphasizing how structural motifs such as wettability gradients, directional transport, and hierarchical porosity have been translated into engineered fog‐collection and vapor‐sorption strategies for enhanced water uptake, accelerated transport, and energy‐efficient ...
Lee Y, Fan S, Yang S.
europepmc   +2 more sources

On some 3 × 3 dimensional matrices associated with generalized Fibonacci numbers

Notes on Number Theory and Discrete Mathematics, 2021
In this work, it is presented a procedure to find some 3 × 3 dimensional matrices whose integer powers can be characterized by generalized Fibonacci numbers. Moreover, some numerical examples are given to exemplify the procedure established.
H. Özdemir, Sinan Karakaya, T. Petik
semanticscholar   +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

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

GCD of Sums of k Consecutive Squares of Generalized Fibonacci Numbers

The Fibonacci quarterly, 2022
In 2021, Guyer and Mbirika gave two equivalent formulas that computed the greatest common divisor (GCD) of all sums of k consecutive terms in the generalized Fibonacci sequence ( G n ) n ≥ 0 given by the recurrence G n = G n − 1 + G n − 2 for all n ≥ 2 ...
A. Mbirika, Jürgen Spilker
semanticscholar   +1 more source

An Alternating Sum of Fibonacci and Lucas Numbers of Order k

Mathematics, 2020
During the last decade, many researchers have focused on proving identities that reveal the relation between Fibonacci and Lucas numbers. Very recently, one of these identities has been generalized to the case of Fibonacci and Lucas numbers of order k ...
Spiros D. Dafnis, Andreas N. Philippou, Ioannis E. Livieris   +2 more
doaj   +1 more source

On Linear Differential Equations Involving a Para-Grassmann Variable [PDF]

, 2009
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly.
Mansour, Toufik, Schork, Matthias
core   +5 more sources

On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3 [PDF]

International Journal of Number Theory, 2019
For an integer [Formula: see text], let [Formula: see text] be the [Formula: see text]-generalized Fibonacci sequence which starts with [Formula: see text] (a total of [Formula: see text] terms) and for which each term afterwards is the sum of the ...
M. Ddamulira, F. Luca
semanticscholar   +1 more source