The Fibonacci–Circulant Sequences and Their Applications

Devecı, Ömür; Karaduman, Erdal; Campbell, C. M.

doi:10.1007/s40995-017-0317-7

Cited by 26 publications

(16 citation statements)

References 10 publications

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“…Recently, there have been so many studies of the sequences of numbers in the literature and the sequences of numbers were widely used in many research areas, such as architecture, nature, art, physics and engineering. For example, in the articles [9], [10], [11] and [12], the authors defined some linear recurrence sequences and investigate their various properties.…”

Section: Resultsmentioning

confidence: 99%

On Summing Formulas of Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

Soykan

2019

ARJOM

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In this paper, we present linear summation formulas for generalized Hexanacci numbers and generalized Gaussian Hexanacci numbers. Also, as special cases, we give linear summation formulas of Hexanacci and Hexanacci-Lucas numbers; Gaussian Hexanacci and Gaussian Hexanacci-Lucas numbers. We present the proofs to indicate how these formulas, in general, were discovered. In fact, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.

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Section: Resultsmentioning

confidence: 99%

On Summing Formulas of Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

Soykan

2019

ARJOM

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“…Many authors use matrix methods in their work. For example, in the articles [10], [11], [12], [13] and [14], the authors defined some linear recurrence sequences and gave their various properties by matrix methods. On the other hand, the matrix sequences have taken so much interest for different type of numbers.…”

Section: Resultsmentioning

confidence: 99%

On A Generalized Pentanacci Sequence

Soykan

2019

ARJOM

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“…For detailed information about the k-step Fibonacci sequence, see [9,21]. In [5], Deveci et al defined the Fibonacci-circulant sequence of the second kind as shown:…”

Section: Introductionmentioning

confidence: 99%

On the Generalized Fibonacci-circulant-Hurwitz numbers

Devecı¹,

Adıgüzel²,

Doğan³

2020

NNTDM

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The theory of Fibonacci-circulant numbers was introduced by Deveci et al. (see [5]). In this paper, we define the Fibonacci-circulant-Hurwitz sequence of the second kind by Hurwitz matrix of the generating function of the Fibonacci-circulant sequence of the second kind and give a fair generalization of the sequence defined, which we call the generalized Fibonacci-circulant-Hurwitz sequence. First, we derive relationships between the generalized Fibonacci-circulant-Hurwitz numbers and the generating matrices for these numbers. Also, we give miscellaneous properties of the generalized Fibonacci-circulant-Hurwitz numbers such as the Binet formula, the combinatorial, permanental, determinantal representations, the generating function, the exponential representation and the sums.

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The Fibonacci–Circulant Sequences and Their Applications

Cited by 26 publications

References 10 publications

On Summing Formulas of Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

On Summing Formulas of Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

On A Generalized Pentanacci Sequence

On the Generalized Fibonacci-circulant-Hurwitz numbers

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