The Generalized (s,t)-Sequence and its Matrix Sequence

Yazlık, Yasin; Taşkara, Necati; Uslu, Kemal; Yılmaz, Nazmiye

doi:10.1063/1.3636742

Cited by 13 publications

(11 citation statements)

References 5 publications

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“…In [5], the authors defined (s, t)-Pell and (s, t)-Pell-Lucas sequences and (s, t)-Pell and (s, t)-Pell-Lucas matrix sequences, also gave their some properties. Yazlik et al,in [14], establish generalized (s, t)-matrix sequences and present some important relationships among (s, t)-Fibonacci and (s, t)-Lucas sequences and their matrix sequences. In [16], Yilmaz and Taskara defined the matrix sequences of Padovan and Perrin numbers.…”

Section: Introductionmentioning

confidence: 99%

The matrix sequence in terms of bi-periodic Fibonacci numbers

Coskun¹,

Taşkara²

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we define the bi-periodic Fibonacci matrix sequence that represent bi-periodic Fibonacci numbers. Then, we investigate generating function, Binet formula and summations of bi-periodic Fibonacci matrix sequence. After that, we say that some behaviours of bi-periodic Fibonacci numbers also can be obtained by considering properties of this new matrix sequence. Finally, we express that wellknown matrix sequences, such as Fibonacci, Pell, k-Fibonacci matrix sequences are special cases of this generalized matrix sequence.

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Section: Introductionmentioning

confidence: 99%

The matrix sequence in terms of bi-periodic Fibonacci numbers

Coskun¹,

Taşkara²

2019

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…On the other hand, the matrix sequences have taken so much interest for di¤erent type of numbers. For matrix sequences of generalized Horadam type numbers, see for example [2], [3], [5], [15], [16], [17], [18], [23], and for matrix sequences of generalized Tribonacci type numbers, see for instance [1], [12], [13], [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Matrix Sequences of Tetranacci and Tetranacci-Lucas Numbers

Soykan¹

2019

Preprint

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“…On the other hand, the matrix sequences have taken so much interest for different type of numbers ( [2,3,4,7,9,12,14,16]). In [4], the authors defined bi-periodic Fibonacci matrix sequence and obtained nth general term of this matrix sequence as…”

Section: Introductionmentioning

confidence: 99%

A note on the bi-periodic Fibonacci and Lucas matrix sequences

Coskun

Taşkara

2018

Applied Mathematics and Computation

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In this paper, we introduce the bi-periodic Lucas matrix sequence and present some fundamental properties of this generalized matrix sequence. Moreover, we investigate the important relationships between the bi-periodic Fibonacci and Lucas matrix sequences. We express that some behaviours of bi-periodic Lucas numbers also can be obtained by considering properties of this new matrix sequence. Finally, we say that the matrix sequences as Lucas, k-Lucas and Pell-Lucas are special cases of this generalized matrix sequence.

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The Generalized (s,t)-Sequence and its Matrix Sequence

Cited by 13 publications

References 5 publications

The matrix sequence in terms of bi-periodic Fibonacci numbers

The matrix sequence in terms of bi-periodic Fibonacci numbers

Matrix Sequences of Tetranacci and Tetranacci-Lucas Numbers

A note on the bi-periodic Fibonacci and Lucas matrix sequences

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