SOME PROPERTIES OF THE GENERALIZED FIBONACCI SEQUENCE {q<sub>n</sub>} BY MATRIX METHODS

Jun, Sang Pyo; Choi, Kwang Ho

doi:10.11568/kjm.2016.24.4.681

Cited by 9 publications

(9 citation statements)

References 13 publications

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“…In [8] koken and Bozkurt studied and defined a Lucas L Q -matrix which is similar to the Fibonacci Q -matrix [9] and the L Qmatrix is defined as where n F and n L are the th n Fibonacci and Lucas numbers, respectively. Jun and Choi in [5] studied the properties of generalized Fibonacci numbers by matrix methods they defined the generalized Fibonacci sequence as…”

Section: Definition 2 [13]mentioning

confidence: 99%

On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods

Wani

Badshah

2017

IJMSC

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In the present paper first and foremost we introduce a generalization of a classical Fibonacci sequence which is called a Fibonacci-Like sequence and at hindmost we obtain some relationships between Lucas sequence and Fibonacci-Like sequence by using two cross two matrix representation to the Fibonacci-Like sequence. The most worth noticing cause of this article is our proof method, since all the identities are proved by using matrix methods.

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Section: Definition 2 [13]mentioning

confidence: 99%

On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods

Wani

Badshah

2017

IJMSC

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“…In the year 2009, a paper entitled, the generalized Fibonacci sequence has been published by Edson and Yayenie [2,3]. Jun, Choi gave some properties of the bi-periodic Fibonacci sequence by using a special matrix in [4]. Bilgici [5] introduced the bi-periodic Lucas sequence into literature in 2014.…”

Section: Introductionmentioning

confidence: 99%

The relations between bi-periodic jacobsthal and bi-periodic jacobsthal lucas sequence

Uygun

2021

Cumhuriyet Science Journal

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In this paper, one of the special integer sequences, Jacobsthal and Jacobsthal Lucas sequences which are encountered in computer science is generalized according to parity of the index of the entries of the sequences, called bi-periodic Jacobsthal and Jacobsthal Lucas sequences. The definitions of the bi-periodic Jacobsthal and Jacobsthal Lucas sequences are given by using classic Jacobsthal and Jacobsthal Lucas sequences. In literature, there were some relations for the bi-periodic Jacobsthal and Jacobsthal Lucas sequences. We find new identities for these sequences. If we substitute = = 1 in the results, we get identities for classic Jacobsthal and Jacobsthal Lucas sequences.

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“…He also found some interesting identities between the above two sequences. The authors in [8], [9], [10], [11], [12], [13], [14], [15] gave interesting properties of bi-periodic sequences.…”

Section: Introductionmentioning

confidence: 99%

A New Generalization of Jacobsthal Lucas Numbers (Bi-Periodic Jacobsthal Lucas Sequence)

Uygun

Owusu

2020

JAMCS

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In this study, we bring into light a new generalization of the Jacobsthal Lucas numbers, which shall also be called the bi-periodic Jacobsthal Lucas sequence as with initial conditions $$\ \hat{c}_{0}=2,\ \hat{c}_{1}=a.$$ The Binet formula as well as the generating function for this sequence are given. The convergence property of the consecutive terms of this sequence is examined after which the well known Cassini, Catalan and the D'ocagne identities as well as some related summation formulas are also given.

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SOME PROPERTIES OF THE GENERALIZED FIBONACCI SEQUENCE {q_n} BY MATRIX METHODS

Abstract: Abstract. In this note, we consider a generalized Fibonacci sequence {q n }. We give a generating matrix for {q n }. With the aid of this matrix, we derive and re-prove some properties involving terms of this sequence

Cited by 9 publications

References 13 publications

On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods

On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods

The relations between bi-periodic jacobsthal and bi-periodic jacobsthal lucas sequence

A New Generalization of Jacobsthal Lucas Numbers (Bi-Periodic Jacobsthal Lucas Sequence)

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SOME PROPERTIES OF THE GENERALIZED FIBONACCI SEQUENCE {qn} BY MATRIX METHODS

Abstract: Abstract. In this note, we consider a generalized Fibonacci sequence {q n }. We give a generating matrix for {q n }. With the aid of this matrix, we derive and re-prove some properties involving terms of this sequence

Cited by 9 publications

References 13 publications

On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods

On the Relations between Lucas Sequence and Fibonacci-like Sequence by Matrix Methods

The relations between bi-periodic jacobsthal and bi-periodic jacobsthal lucas sequence

A New Generalization of Jacobsthal Lucas Numbers (Bi-Periodic Jacobsthal Lucas Sequence)

Contact Info

Product

Resources

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SOME PROPERTIES OF THE GENERALIZED FIBONACCI SEQUENCE {q_n} BY MATRIX METHODS