Anthony G. Shannon, Özgür Erdağ and Ömür Deveci

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 1, Pages 148—160

DOI: 10.7546/nntdm.2021.27.1.148-160

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## Details

### Authors and affiliations

Anthony G. Shannon

*Warrane College, University of New South Wales
Kensington, Australia
*

Özgür Erdağ

*Department of Mathematics, Faculty of Science and Letters
Kafkas University 36100, Turkey
*

Ömür Deveci

*Department of Mathematics, Faculty of Science and Letters
Kafkas University 36100, Turkey
*

### Abstract

In this paper, we define the Fibonacci–Pell *p*-sequence and then we discuss the connection of the Fibonacci–Pell *p*-sequence with the Pell and Fibonacci *p*-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Fibonacci–Pell *p*-numbers by the aid of the *n*-th power of the generating matrix of the Fibonacci–Pell *p*-sequence. Furthermore, we derive relationships between the Fibonacci–Pell *p*-numbers and their permanent, determinant and sums of certain matrices.

### Keywords

- Pell sequence
- Fibonacci
*p*-sequence - Matrix
- Representation

### 2010 Mathematics Subject Classification

- 11K31
- 11C20
- 15A15

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Mathematical and Computer Modelling, 52(9–10), 1763–1770..

## Related papers

- Shannon, A. G., Horadam, A. F., & Anderson, P. G. (2006). The auxiliary equation associated with the plastic number.
*Notes on Number Theory and Discrete Mathematics*, 12(1), 1–12. - Deveci, Ö., Adigüzel, Z. & Doğan, T. (2020). On the Generalized Fibonacci-circulant-Hurwitz numbers. Notes on Number Theory and Discrete Mathematics, 26(1), 179–190.
- Mehraban, E., & Hashemi, M. (2023). Coding theory on the generalized balancing sequence.
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## Cite this paper

Shannon, A.G., Erdağ, Ö., & Deveci, Ö. (2021). On the connections between Pell numbers and Fibonacci *p*-numbers. Notes on Number Theory and Discrete Mathematics, 27(1), 148-160, doi: 10.7546/nntdm.2021.27.1.148-160.