Results 21 to 30 of about 1,029,498 (122)

The mathematics of generalized Fibonacci sequences: Binet's formula and identities [PDF]

Mathematica Moravica
This article considers a generalized Fibonacci sequence {Vn} with general initial conditions, V0 = a, V1 = b, and a versatile recurrence relation Vn = pVn-1 + qVn-2, where n ≥ 2 and a, b, p and q are any non-zero real numbers. The generating function and
Verma K.L.
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On the Bicomplex $k$-Fibonacci Quaternions

Communications in Advanced Mathematical Sciences, 2019
In this paper, bicomplex $k$-Fibonacci quaternions are defined. Also, some algebraic properties of bicomplex $k$-Fibonacci quaternions are investigated.
Fügen Torunbalcı Aydın
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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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The Generalization of Gaussians and Leonardo’s Octonions

Annales Mathematicae Silesianae, 2023
In order to explore the Leonardo sequence, the process of complex-ification of this sequence is carried out in this work. With this, the Gaussian and octonion numbers of the Leonardo sequence are presented.
Vieira Renata Passos Machado, dos Santos Mangueira Milena Carolina, Alves Francisco Régis Vieira, Catarino Paula Maria Machado Cruz   +3 more
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Dual-Gaussian Pell and Pell-Lucas numbers

Cumhuriyet Science Journal, 2022
In this study, we define a new type of Pell and Pell-Lucas numbers which are called dual-Gaussian Pell and dual-Gaussian Pell-Lucas numbers. We also give the relationship between negadual-Gaussian Pell and Pell-Lucas numbers and dual-complex Pell
Hasan Gökbaş
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On the Lichtenberg hybrid quaternions [PDF]

Mathematica Moravica
In this study, we define Lichtenberg hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formulas of these quaternions. We find some relations between Jacobsthal hybrid quaternions, Mersenne
Morales Gamaliel
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On the Products of k-Fibonacci Numbers and k-Lucas Numbers

International Journal of Mathematics and Mathematical Sciences, 2014
In this paper we investigate some products of k-Fibonacci and k-Lucas numbers. We also present some generalized identities on the products of k-Fibonacci and k-Lucas numbers to establish connection formulas between them with the help of Binet's formula.
Bijendra Singh, Kiran Sisodiya, Farooq Ahmad   +2 more
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On Bicomplex Pell and Pell-Lucas Numbers

Communications in Advanced Mathematical Sciences, 2018
In this paper, bicomplex Pell and bicomplex Pell-Lucas numbers are defined. Also, negabicomplex Pell and negabicomplex Pell-Lucas numbers are given. Some algebraic properties of bicomplex Pell and bicomplex Pell-Lucas numbers which are connected between ...
Fügen Torunbalcı Aydın
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Gaussian Generalized Tetranacci Numbers

, 2019
In this paper, we define Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their ...
Soykan, Yüksel
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Generalized Identities Involving Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas Numbers

International Journal of Analysis and Applications, 2013
In this paper, we present generalized identities involving common factors of generalized Fibonacci, Jacobsthal and jacobsthal-Lucas numbers. Binet’s formula will employ to obtain the identities.
Yashwant K. Panwar, Bijendra Singh, V. K. Gupta   +2 more
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