**Orhan Dişkaya and Hamza Menken**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 1, Pages 1–7

DOI: 10.7546/nntdm.2024.30.1.1-7

**Full paper (PDF, 182 Kb)**

## Details

### Authors and affiliations

Orhan Dişkaya

*Department of Mathematics, Mersin University
Mersin, Turkey*

Hamza Menken

*Department of Mathematics, Mersin University
Mersin, Turkey*

### Abstract

A novel kind of Padovan sequence is introduced, and precise formulas for the form of its members are given and proven. Furthermore, the pulsating Padovan sequence in its most general form is introduced and the obtained identity is proved.

### Keywords

- Fibonacci sequence
- Jacobsthal sequence
- Padovan sequence

### 2020 Mathematics Subject Classification

- 11B39

### References

- Atanassov, K. (2013). Pulsating Fibonacci sequences.
*Notes on Number Theory and Discrete Mathematics*, 19(3), 12–14. - Atanassov, K. (2013). Pulsated Fibonacci sequence. Part 2.
*Notes on Number Theory and Discrete Mathematics*, 19(4), 33–36. - Atanassov, K. T. (2014).
*n*-Pulsated Fibonacci sequence.*Notes on Number Theory and Discrete Mathematics*, 20(1), 32–35. - Atanassov, K., Deford, D. R., Shannon, A. G., & Atanassov, K. (2014). Pulsated Fibonacci recurrences.
*The Fibonacci Quarterly*, 52(5), 22–27. - Atanassov, K., Atanassova, V., Shannon, A., & Turner, J. (2002).
*New Visual Perspectives on Fibonacci Numbers*. World Scientific, New Jersey. - Horadam, A. F. (1996). Jacobsthal representation numbers.
*The Fibonacci Quarterly*, 34(1), 40–54. - Karatas¸, A., & Halıcı, S. (2019). On complex pulsating Fibonacci sequence.
*Konuralp Journal of Mathematics*, 7(2), 274–278. - Khachorncharoenkul, P., Phibul, K., & Laipaporn, K. (2022). The complex pulsating (
*a*_{1},*a*_{2}, …,*a*,_{m}*c*)-Fibonacci sequence.*Journal of King Saud University-Science*, 34(5), 102063. - Koshy, T. (2018).
*Fibonacci and Lucas Numbers with Applications. Volume 1.*John Wiley & Sons, New Jersey. - Koshy, T. (2019).
*Fibonacci and Lucas Numbers with Applications. Volume 2.*John Wiley & Sons, New Jersey. - Laipaporn, K., Phibul, K., & Khachorncharoenkul, P. (2022). The metallic ratio of pulsating Fibonacci sequences.
*Symmetry*, 14(6), 1204. - Laipaporn, K., Phibul, K., & Khachorncharoenkul, P. (2021). On the pulsating (
*m*,*c*)-Fibonacci sequence.*Heliyon*, 7(9), e07883. - Suvarnamani, A. (2017). On the multiplicative pulsating
*n*-Fibonacci sequence.*SNRU Journal of Science and Technology*, 9(2), 502–508.

### Manuscript history

- Received: 29 June 2022
- Revised: 8 May 2023
- Accepted: 18 February 2024
- Online First: 22 February 2024

### Copyright information

Ⓒ 2024 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

## Related papers

- Atanassov, K. (2013). Pulsating Fibonacci sequences.
*Notes on Number Theory and Discrete Mathematics*, 19(3), 12–14. - Atanassov, K. (2013). Pulsated Fibonacci sequence. Part 2.
*Notes on Number Theory and Discrete Mathematics*, 19(4), 33–36. - Atanassov, K. T. (2014).
*n*-Pulsated Fibonacci sequence.*Notes on Number Theory and Discrete Mathematics*, 20(1), 32–35.

## Cite this paper

Dişkaya, O., & Menken, H. (2024). On the pulsating Padovan sequence. *Notes on Number Theory and Discrete Mathematics*, 30(1), 1-7, DOI: 10.7546/nntdm.2024.30.1.1-7.