ON THE A NEW FAMILY OF k-FIBONACCI NUMBERS

Taşyurdu, Yasemin; Çobanoğlu, Nurdan; Dilmen, Zülküf

doi:10.18185/eufbed.01209

Cited by 14 publications

(10 citation statements)

References 10 publications

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“…In particular, many various generalizations of this sequence have been studied in the literature. (see, for example, McCarty, 1981;Pethe, 1988;Koshy, 2001;Gupta et al, 2012a;Taşyurdu, 2016). The Tribonacci and Tribonacci-Lucas sequences, which are the well-known generalizations of Fibonacci sequences, are third order recurrence sequences.…”

Section: Introductionmentioning

confidence: 99%

Tribonacci and Tribonacci-Lucas Hybrinomials

Taşyurdu¹,

Polat²

2021

JMR

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Section: Introductionmentioning

confidence: 99%

Tribonacci and Tribonacci-Lucas Hybrinomials

Taşyurdu¹,

Polat²

2021

JMR

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“…Some authors defined various -Fibonacci-like sequences. It has obtained a lot of study on the new family of -Fibonacci sequences, -Lucas sequences (Panwar, 2014;Tasyurdu, 2016;Wani et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Generalized (p,q)-Fibonacci-Like Sequences and Their Properties

Taşyurdu¹

2019

JMR

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In this paper, we define the generalized (p,q) -Fibonacci-Like sequences Sp,q,n  associated with the (p,q) -Fibonacci and the (p,q) -Lucas sequences and then we get some fundamental identities and sums formulas involving odd and even terms of the generalized (p,q) -Fibonacci-Like sequences. We obtain the Binet's formula to find the n th general term of generalized (p,q) -Fibonacci-Like sequences Sp,q,n . Also, the generating functions of these sequences are presented and proved.In this paper, we define the generalized (p,q) -Fibonacci-Like sequences Sp,q,n  associated with the (p,q) -Fibonacci and the (p,q) -Lucas sequences and then we get some fundamental identities and sums formulas involving odd and even terms of the generalized (p,q) -Fibonacci-Like sequences. We obtain the Binet's formula to find the n th general term of generalized (p,q) -Fibonacci-Like sequences Sp,q,n . Also, the generating functions of these sequences are presented and proved.

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“…Fibonacci n F and Lucas n L sequences, ones of the most important members of integer sequences, are also associated with a lot of polynomials (Koshy,2001) and some sequences. (McDaniel,1991;Chen,2011, Tasyurdu et al,2016Karakas,2017;Gül,2018).…”

Section: Introductionmentioning

confidence: 99%

Değiştirilmiş Pell ve Pell Lucas Dizilerinin Özellikleri

Köken

2019

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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The altered Pell and Pell Lucas sequences are defined by altering the Pell and Pell Lucas numbers, it is seen that they have similar properties to usual the Pell and Pell Lucas sequences. Thus, we study some recursive properties of the altered sequences. Further, the greatest common divisors (i.e. GCD) sequences of the altered sequences are investigated, and it is seen that the GCD sequences are subsequences of the Pell and Pell Lucas sequences. Therefore, we obtain Binet formula, the Cassini, Catalan and D'ocagne's identities of the GCD sequences.

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ON THE A NEW FAMILY OF k-FIBONACCI NUMBERS

Cited by 14 publications

References 10 publications

Tribonacci and Tribonacci-Lucas Hybrinomials

Tribonacci and Tribonacci-Lucas Hybrinomials

Generalized (p,q)-Fibonacci-Like Sequences and Their Properties

Değiştirilmiş Pell ve Pell Lucas Dizilerinin Özellikleri

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