The Hadamard-type <i>k</i>-step Fibonacci sequences in groups

Aküzüm, Yeşim; Devecı, Ömür

doi:10.1080/00927872.2020.1723609

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2024

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Cited by 5 publications

(2 citation statements)

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“…Fibonacci sequence and its generalization t-Fibonacci sequence are famous sequences in mathematics. Many authors studied on these sequences (for example [1,2,5,6,9,12,18,19]). For t ≥ 2, the t-Fibonacci number sequence, {F t n } ∞ n=0 , is defined by…”

Section: Introductionmentioning

confidence: 99%

The t-Fibonacci sequences in the 2-generator p-groups of nilpotency class 2

Mehraban,

Deveci,

Hincal

2023

NNTDM

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Section: Introductionmentioning

confidence: 99%

The t-Fibonacci sequences in the 2-generator p-groups of nilpotency class 2

Mehraban,

Deveci,

Hincal

2023

NNTDM

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“…, are related to the enumeration of fatty acids in [27]. Number sequences are generalized in different ways, see [1,16,17,19,[21][22][23][24]. As a result of obtaining k-Fibonacci sequences, which are the more general versions of Fibonacci sequences, and by defining the distance of the sequences, it was possible to switch to r-distance (k, r)-Fibonacci sequences.…”

Section: Introductionmentioning

confidence: 99%

On generalized (k, r)-Pell and (k, r)-Pell–Lucas numbers

Kuloğlu¹,

Özkan²

2022

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We introduce new kinds of k-Pell and k-Pell–Lucas numbers related to the distance between numbers by a recurrence relation and show their relation to the (k,r)-Pell and (k,r)-Pell–Lucas numbers. These sequences differ both according to the value of the natural number k and the value of a new parameter r in the definition of this distance. We give several properties of these sequences. In addition, we establish the generating functions, some important identities, as well as the sum of the terms of the generalized (k,r)-Pell and (k,r)-Pell–Lucas numbers. Furthermore, we indicate another way to obtain the generalized (k,r)-Pell and (k,r)-Pell–Lucas sequences from the generating function, in connection to graphs.

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