Results 11 to 20 of about 976 (217)
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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Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences [PDF]
Kyungpook mathematical journal, 2017 In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where $p$ is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, $m$ and derive certain interesting properties related to them.
Laugier, Alexandre, Saikia, Manjil P.
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Curious Generalized Fibonacci Numbers [PDF]
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 +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 The Generalized Gaussian Fibonacci Numbers. [PDF]
Ars Comb., 2017 Many authors define certain generalizations of the usual Fibonacci, Pell and Lucas numbers by matrix methods and then obtain the Binet formulas and combinatorial representations of the generalizations of these number sequence. In this article firstly we define and study the generalized Gaussian Fibonacci numbers and then find the matrix representation ...
Lee, G.Y., Aşçı, Mustafa
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Carlitz’s Equations on Generalized Fibonacci Numbers [PDF]
Symmetry, 2022 Carlitz solved some Diophantine equations on Fibonacci or Lucas numbers. We extend his results to the sequence of generalized Fibonacci and Lucas numbers. In this paper, we solve the Diophantine equations of the form An1⋯Ank=Bm1⋯BmrCt1⋯Cts, where (An), (Bm), and (Ct) are generalized Fibonacci or Lucas numbers.
Min Wang, Peng Yang 0019, Yining Yang
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On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers [PDF]
Advances in Research, 2019 In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers and ...
Yüksel Soykan, Soykan, Yüksel
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MathematicsThis paper presents a comprehensive survey of the generalization of hybrid numbers and hybrid polynomials, particularly in the fields of mathematics and physics.
Can Kızılateş +2 more
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Corrigendum: On Summing Formulas for Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers [PDF]
Advances in Research, 2020 In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers and ...
Soykan, Y¨uksel, Y¨uksel Soykan
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