Results 41 to 50 of about 1,420,930 (275)

Closed Formulas for the Sums of Squares of Generalized Fibonacci Numbers

, 2020
In this paper, closed forms of the sum formulas for the squares of generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas numbers.
Y. Soykan
semanticscholar   +1 more source

Bounds for a new subclass of bi-univalent functions subordinate to the Fibonacci numbers

Turkish Journal of Mathematics, 2020
In this investigation, by using a relation of subordination, we define a new subclass of analytic bi-univalent functions associated with the Fibonacci numbers. Moreover, we survey the bounds of the coefficients for functions in this class.
Ş. Altınkaya
semanticscholar   +1 more source

Generalized Fibonacci Numbers: Sum Formulas

Journal of Advances in Mathematics and Computer Science, 2020
In this paper, closed forms of the summation formulas for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.
Y. Soykan
semanticscholar   +1 more source

On Distance (r,k)-Fibonacci Numbers and Their Combinatorial and Graph Interpretations

Journal of Applied Mathematics, 2015
We introduce three new two-parameter generalizations of Fibonacci numbers. These generalizations are closely related to k-distance Fibonacci numbers introduced recently. We give combinatorial and graph interpretations of distance (r,k)-Fibonacci numbers.
Dorota Bród
doaj   +1 more source

Periodic words connected with the Fibonacci words

Karpatsʹkì Matematičnì Publìkacìï, 2016
In this paper we introduce two families of periodic words (FLP-words of type 1 and FLP-words of type 2) that are connected with the Fibonacci words and investigated their properties.
G.M. Barabash, Ya.M. Kholyavka, I.V. Tytar   +2 more
doaj   +1 more source

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

On New Formulas of Fibonacci and Lucas Numbers Involving Golden Ratio Associated with Atomic Structure in Chemistry

Symmetry, 2021
The main purpose of this paper is to give many new formulas involving the Fibonacci numbers, the golden ratio, the Lucas numbers, and other special numbers.
Rifat Battaloğlu, Y. Simsek
semanticscholar   +1 more source

Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials

Discrete Dynamics in Nature and Society, 2012
We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci, Mirac Cetin Firengiz, Naim Tuglu   +2 more
doaj   +1 more source

A Study on Dual Hyperbolic Fibonacci and Lucas Numbers

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019
In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers.
Cihan Arzu, Azak Ayşe Zeynep, Güngör Mehmet Ali, Tosun Murat   +3 more
doaj   +1 more source

Curious Generalized Fibonacci Numbers

Mathematics, 2021
A generalization of the well-known Fibonacci sequence is the k−Fibonacci sequence whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci numbers that are curious numbers (i.e.,
Jose L. Herrera, Jhon J. Bravo, Carlos A. Gómez   +2 more
doaj   +1 more source