Results 11 to 20 of about 30,143 (265)

On Generalized Jacobsthal and Jacobsthal–Lucas Numbers

Annales Mathematicae Silesianae, 2022
Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
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Some identities for generalized Fibonacci and Lucas numbers

AKCE International Journal of Graphs and Combinatorics, 2020
In this paper we study one parameter generalization of the Fibonacci numbers, Lucas numbers which generalizes the Jacobsthal numbers, Jacobsthal–Lucas numbers simultaneously. We present some their properties and interpretations also in graphs.
Anetta Szynal-Liana, Iwona Włoch, Mirosław Liana   +2 more
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Gaussian-bihyperbolic Numbers Containing Pell and Pell-Lucas Numbers

Journal of Advanced Research in Natural and Applied Sciences, 2023
In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-bihyperbolic Pell and Pell-Lucas numbers. We also define negaGaussian-bihyperbolic Pell and Pell-Lucas numbers.
Hasan Gökbaş
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On properties of generalized Tridovan numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this paper, we examine generalized Tridovan sequences and treat in detail two cases called Tridovan sequences and Tridovan–Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these ...
Yüksel Soykan, Nejla Özmen, İnci Okumuş   +2 more
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The GCD Sequences of the Altered Lucas Sequences

Annales Mathematicae Silesianae, 2020
In this study, we give two sequences {L+n}n≥1 and {L−n}n≥1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers.
Koken Fikri
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Solutions of equations x2−(p2q2±3p)y2=±kt

Examples and Counterexamples, 2022
In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences.
Roji Bala, Vinod Mishra
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Unrestricted Tribonacci and Tribonacci–Lucas quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
We define a generalization of Tribonacci and Tribonacci–Lucas quaternions with arbitrary Tribonacci numbers and Tribonacci–Lucas numbers coefficients, respectively. We get generating functions and Binet's formulas for these quaternions.
Gonca Kızılaslan, Leyla Karabulut
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Hybrid hyper-Fibonacci and hyper-Lucas numbers [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
Different number systems have been studied lately. Recently, many researchers have considered the hybrid numbers which are generalization of the complex, hyperbolic and dual number systems.
Yasemin Alp
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On tridimensional Lucas-balancing numbers and some properties [PDF]

Notes on Number Theory and Discrete Mathematics
In this article, we introduce the tridimensional version of the Lucas-balancing numbers based on the unidimensional version, and we also study some of their properties and sum identities.
J. Chimpanzo, P. Catarino, M. V. Otero-Espinar   +2 more
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Incomplete Tribonacci–Lucas Numbers and Polynomials [PDF]

Advances in Applied Clifford Algebras, 2014
In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence relations, some properties and generating functions of these numbers and polynomials. Also, we find the generating function
Yilmaz, Nazmiye, Taskara, Necati
openaire   +2 more sources