**Lilija Atanassova and Velin Andonov**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 3, Pages 634–639

DOI: 10.7546/nntdm.2024.30.3.634-639

Full paper (PDF, 163 Kb)

## Details

### Authors and affiliations

Lilija Atanassova

*Institute of Information and Communication Technologies, Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 2, Sofia 1113, Bulgaria*

Velin Andonov

*Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 8, Sofia 1113, Bulgaria*

### Abstract

A new Fibonacci sequence from a pulsated type is introduced. The explicit form of its members is given.

### Keywords

- Fibonacci sequence
- Pulsated sequence

### 2020 Mathematics Subject Classification

- 11B39

### References

- Atanassov, K. (1985). An arithmetic function and some of its applications.
*Bulletin of Number Theory and Related Topics*, 9, 18–27. - Atanassov, K. (1986). On a second new generalization of the Fibonacci sequence.
*The Fibonacci Quarterly*, 24(4), 362–365. - Atanassov, K. (1989). On a generalization of the Fibonacci sequence in the case of three sequences.
*The Fibonacci Quarterly*, 27(1), 7–10. - Atanassov, K. (2010). Combined 2-Fibonacci sequences.
*Notes on Number Theory and Discrete Mathematics*, 16(2), 24–28. - Atanassov, K. (2013). Pulsating Fibonacci sequence. 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. (2014).
*n*-Pulsated Fibonacci sequence.*Notes on Number Theory and Discrete Mathematics*, 20(1), 32–35. - Atanassov, K. (2017). On two new two-dimensional extensions of the Fibonacci sequence.
*Notes on Number Theory and Discrete Mathematics*, 23(3), 115–122. - Atanassov, K. (2018). On two new combined 3-Fibonacci sequences.
*Notes on Number Theory and Discrete Mathematics*, 24(2), 90–93. - Atanassov, K. (2021). A short remark on a new Fibonacci-type sequence.
*Notes on Number Theory and Discrete Mathematics*, 27(2), 168–171. - Atanassov, K., Atanassova, L. & Sasselov, D. (1985). A new perspective to the generalization of the Fibonacci sequence.
*The Fibonacci Quarterly*, 23(1), 21–28. - Atanassov, K., Atanassova, V., Shannon, A., & Turner, J. (2002).
*New Visual Perspectives on Fibonacci Numbers*. World Scientific, New Jersey. - Atanassov, K., Deford, D. R., & Shannon, A. G. (2014). Pulsated Fibonacci recurrences. In:
*Anderson, P., Ballot, C., & Webb, W. (Eds.). Proceedings of the Sixteenth International Conference on Fibonacci Numbers and Their Applications*, July 20–27 2014, Rochester, New York, 22–27. - Atanassov, K., & Dimitrov, D. (2010). On
*ψ*-function and 2-Fibonacci sequences.*Notes on Number Theory and Discrete Mathematics*, 16(1), 5–48. - Atanassov, K., & Shannon, A. G. (2005). Digit sum bases for Fibonacci and related numbers.
*Notes on Number Theory and Discrete Mathematics*, 11(3), 25–32. - Atanassov, K., & Shannon, A. G. (2016). Combined 3-Fibonacci sequences from a new type.
*Notes on Number Theory and Discrete Mathematics*, 22(3), 5–8. - Atanassova, L., & Andonov, V. (2023). New Fibonacci-type pulsated sequences.
*Notes on Number Theory and Discrete Mathematics*, 29(4), 789–793. - Lee, J.-Z., & Lee, J.-S. (1987). Some properties of the generalization of the Fibonacci sequence.
*The Fibonacci Quarterly*, 25(2), 111–117. - Spickerman, W., & Creech, R. (1997). The (2,
*T*) generalized Fibonacci sequences.*The Fibonacci Quarterly*, 35(4), 358–360. - Spickerman, W., Creech, R., & Joyner, R. (1993). On the structure of the set of difference systems defining (3,
*F*) generalized Fibonacci sequence.*The Fibonacci Quarterly*, 31(4), 333–337. - Spickerman, W., Creech, R., & Joyner, R. (1995). On the (3,
*F*) generalizations of the Fibonacci sequence.*The Fibonacci Quarterly*, 33(1), 9–12. - Spickerman, W., Joyner, R., & Creech, R. (1992). On the (2,
*F*)-generalizations of the Fibonacci sequence.*The Fibonacci Quarterly*, 30(4), 310–314.

### Manuscript history

- Received: 22 February 2024
- Revised: 29 August 2024
- Accepted: 16 October 2024
- Online First: 24 October 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

## Cite this paper

Atanassova, L., & Andonov, V. (2024). New Fibonacci-type pulsated sequences. Part 2. *Notes on Number Theory and Discrete Mathematics*, 30(3), 634-639, DOI: 10.7546/nntdm.2024.30.3.634-639