Hessenberg matrices and the Pell and Perrin numbers

Yılmaz, Fatih; Bozkurt, Durmuş

doi:10.1016/j.jnt.2011.02.002

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Cited by 35 publications

(21 citation statements)

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“…Now we introduce a Pell number sequence [3,10,[17][18][19] that plays a very important role in our main results. The Pell number P n satisfies the following recurrence:…”

Section: Introductionmentioning

confidence: 99%

On determinants and inverses of some triband Toeplitz matrices with permuted columns

Li¹,

Jiang²,

Zheng³

2019

J. Math. Computer Sci.

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“…Now we introduce a Pell number sequence [3,10,[17][18][19] that plays a very important role in our main results. The Pell number P n satisfies the following recurrence:…”

Section: Introductionmentioning

confidence: 99%

On determinants and inverses of some triband Toeplitz matrices with permuted columns

Li¹,

Jiang²,

Zheng³

2019

J. Math. Computer Sci.

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“…Xu and Zhou [26] studied a determinantal representation for a generalization of the Stirling numbers, called r-Whitney numbers, see also [19]. More examples can be found in [23,24,27].…”

Section: Introductionmentioning

confidence: 99%

Some Determinants Involving Incomplete Fubini Numbers

Komatsu

Ramírez

2018

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…Yilmaz and Bozkurt [25] gave matrix representation of Perrin sequences. Kaygisiz and Sahin [10] calculated terms of associated polynomials of Perrin and Cordonnier numbers by using determinants and permanents of various Hessenberg matrices.…”

Section: Introductionmentioning

confidence: 99%

On the generalized Perrin and Cordonnier matrices

Sahin

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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C o m m u n . Fa c . S c i. U n iv . A n k . S é r. A 1 M a th . S ta t. Vo lu m e 6 6 , N u m b e r 1 , P a g e s 2 4 2 -2 5 3 (2 0 1 7 ) D O I: 1 0 .1 5 0 1 / C o m m u a 1 _ 0 0 0 0 0 0 0 7 9 3 IS S N 1 3 0 3 -5 9 9 1 ON THE GENERALIZED PERRIN AND CORDONNIER MATRICES ADEMŞAH · INAbstract. In the present paper, we study the associated polynomials of Perrin and Cordonnier numbers. We de…ne generalized Perrin and Cordonnier matrices using these polynomials. We obtain the inverse of generalized Cordonnier matrices and give some relationships between generalized Perrin and Cordonnier matrices. In addition, we give a factorization of generalized Cordonnier matrices. Finally, we give some determinantal representation of associated polynomials Cordonnier numbers.

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Hessenberg matrices and the Pell and Perrin numbers

Abstract: In this paper, we investigate the Pell sequence and the Perrin sequence and we derive some relationships between these sequences and permanents and determinants of one type of Hessenberg matrices.

Cited by 35 publications

References 1 publication

On determinants and inverses of some triband Toeplitz matrices with permuted columns

On determinants and inverses of some triband Toeplitz matrices with permuted columns

Some Determinants Involving Incomplete Fubini Numbers

On the generalized Perrin and Cordonnier matrices

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