Results 1 to 10 of about 973 (216)

On the Sum of Reciprocal Generalized Fibonacci Numbers [PDF]

Abstract and Applied Analysis, 2014
We consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.
Pingzhi Yuan, Zilong He, Junyi Zhou
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On (k,p)-Fibonacci Numbers [PDF]

Mathematics, 2021
In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously.
Natalia Bednarz
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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
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On Generalized Fibonacci Numbers

Communications in Advanced Mathematical Sciences, 2020
Fibonacci numbers and their polynomials have been generalized mainly by two ways: by maintaining the recurrence relation and varying the initial conditions, and by varying the recurrence relation and maintaining the initial conditions. In this paper, we
Isaac Owino Okoth, Fidel Oduol
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On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

Mathematics
This paper presents a comprehensive survey of the generalization of hybrid numbers and hybrid polynomials, particularly in the fields of mathematics and physics.
Can Kızılateş, Wei-Shih Du, Nazlıhan Terzioğlu   +2 more
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Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals

Mathematics, 2022
The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients for a specific z.
Waleed Mohamed Abd-Elhameed, Andreas N. Philippou, Nasr Anwer Zeyada   +2 more
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On generalized Fibonacci numbers [PDF]

Applied Mathematical Sciences, 2015
We provide a formula for the $n^{th}$ term of the $k$-generalized Fibonacci-like number sequence using the $k$-generalized Fibonacci number or $k$-nacci number, and by utilizing the newly derived formula, we show that the limit of the ratio of successive terms of the sequence tends to a root of the equation $x + x^{-k} = 2$.
Bacani, Jerico B., Rabago, Julius Fergy T.   +1 more
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Notes on generalized and extended Leonardo numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences.
Anthony G. Shannon, Peter J.-S. Shiue, Shen C. Huang   +2 more
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“Generating matrix for Generalized Fibonacci numbers and Fibonacci polynomials

Journal of Physics: Conference Series, 2022
AbstractMany researchers have been working on recurrence relation sequences of numbers and polynomials which are useful topic not only in mathematics but also in physics, economics and various applications in many other fields. There are many useful identities on recurrence relation sequence but there main problem to find any term of recurrence ...
Mannu Arya, Vipin Verma
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The sequence of trifurcating Fibonacci numbers

Ratio Mathematica, 2021
One of the interesting generalizations of Fibonacci sequence is a k-Fibonacci sequence, which is further generalized into the ‘Bifurcating Fibonacci sequence’.
Parimalkumar A. Patel, Dr. Devbhadra V. Shah   +1 more
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