Some Properties between Mersenne, Jacobsthal and Jacobsthal-Lucas Hybrid Numbers

Tasci, Dursun; Sevgi, Emre

doi:10.1016/j.chaos.2021.110862

Cited by 10 publications

(5 citation statements)

References 5 publications

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“…Several studies related to hybrid numbers with different integer sequence coefficients can be found in Refs. [24][25][26][27][28][29][30][31][32], among others. See also the studies cited by these papers.…”

Section: Respectivelymentioning

confidence: 99%

On Gaussian Leonardo Hybrid Polynomials

Yağmur

2023

Symmetry

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In the present paper, we first study the Gaussian Leonardo numbers and Gaussian Leonardo hybrid numbers. We give some new results for the Gaussian Leonardo numbers, including relations with the Gaussian Fibonacci and Gaussian Lucas numbers, and also give some new results for the Gaussian Leonardo hybrid numbers, including relations with the Gaussian Fibonacci and Gaussian Lucas hybrid numbers. For the proofs, we use the symmetric and antisymmetric properties of the Fibonacci and Lucas numbers. Then, we introduce the Gaussian Leonardo polynomials, which can be considered as a generalization of the Gaussian Leonardo numbers. After that, we introduce the Gaussian Leonardo hybrid polynomials, using the Gaussian Leonardo polynomials as coefficients instead of real numbers in hybrid numbers. Moreover, we obtain the recurrence relations, generating functions, Binet-like formulas, Vajda-like identities, Catalan-like identities, Cassini-like identities, and d’Ocagne-like identities for the Gaussian Leonardo polynomials and hybrid polynomials, respectively.

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Section: Respectivelymentioning

confidence: 99%

On Gaussian Leonardo Hybrid Polynomials

Yağmur

2023

Symmetry

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“…The authors considered the hybrid numbers with the Padovan numbers and obtained some identities of these numbers in [16]. Tasci and Sevgi defined the Mersenne hybrid numbers and obtained some relations among the Mersenne, the Jacobsthal and the Jacobsthal-Lucas hybrid numbers in [26]. In [8], the author considered the hybrid numbers with generalization of the Fibonacci numbers and acquired some results.…”

Section: Introductionmentioning

confidence: 99%

“…Taking 𝑚 = −𝑘 and 𝑠 = 𝑘 in (26), it can be obtained the Catalan's identity of the hybrid hyper-Fibonacci numbers as following corollary.…”

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confidence: 99%

Hybrid hyper-Fibonacci and hyper-Lucas numbers

Alp¹

2023

NNTDM

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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. In this paper, we define the hybrid hyper-Fibonacci and hyper-Lucas numbers. Furthermore, we obtain some algebraic properties of these numbers such as the recurrence relations, the generating functions, the Binet’s formulas, the summation formulas, the Catalan’s identity, the Cassini’s identity and the d’Ocagne’s identity.

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“…For example, in [3], the authors get some properties for the Mersenne-Lucas hybrid numbers. In [4], the authors scrutinize some identities for the Mersenne, Jacobsthal and Jacobsthal-Lucas hybrid numbers. The authors obtain some results for the generalized On Hybrid numbers with Gaussian Mersenne Coefficients 214 tetranacci hybrid numbers, in [5].…”

Section: Introductionmentioning

confidence: 99%