New Fibonacci-type pulsated sequences. Part 2

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

  1. Atanassov, K. (1985). An arithmetic function and some of its applications. Bulletin of Number Theory and Related Topics, 9, 18–27.
  2. Atanassov, K. (1986). On a second new generalization of the Fibonacci sequence. The Fibonacci Quarterly, 24(4), 362–365.
  3. Atanassov, K. (1989). On a generalization of the Fibonacci sequence in the case of three sequences. The Fibonacci Quarterly, 27(1), 7–10.
  4. Atanassov, K. (2010). Combined 2-Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 16(2), 24–28.
  5. Atanassov, K. (2013). Pulsating Fibonacci sequence. Notes on Number Theory and Discrete Mathematics, 19(3), 12–14.
  6. Atanassov, K. (2013). Pulsated Fibonacci sequence. Part 2. Notes on Number Theory and Discrete Mathematics, 19(4), 33–36.
  7. Atanassov, K. (2014). n-Pulsated Fibonacci sequence. Notes on Number Theory and Discrete Mathematics, 20(1), 32–35.
  8. Atanassov, K. (2017). On two new two-dimensional extensions of the Fibonacci sequence. Notes on Number Theory and Discrete Mathematics, 23(3), 115–122.
  9. Atanassov, K. (2018). On two new combined 3-Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 24(2), 90–93.
  10. Atanassov, K. (2021). A short remark on a new Fibonacci-type sequence. Notes on Number Theory and Discrete Mathematics, 27(2), 168–171.
  11. Atanassov, K., Atanassova, L. & Sasselov, D. (1985). A new perspective to the generalization of the Fibonacci sequence. The Fibonacci Quarterly, 23(1), 21–28.
  12. Atanassov, K., Atanassova, V., Shannon, A., & Turner, J. (2002). New Visual Perspectives on Fibonacci Numbers. World Scientific, New Jersey.
  13. 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.
  14. Atanassov, K., & Dimitrov, D. (2010). On ψ-function and 2-Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 16(1), 5–48.
  15. 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.
  16. 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.
  17. Atanassova, L., & Andonov, V. (2023). New Fibonacci-type pulsated sequences. Notes on Number Theory and Discrete Mathematics, 29(4), 789–793.
  18. Lee, J.-Z., & Lee, J.-S. (1987). Some properties of the generalization of the Fibonacci sequence. The Fibonacci Quarterly, 25(2), 111–117.
  19. Spickerman, W., & Creech, R. (1997). The (2, T) generalized Fibonacci sequences. The Fibonacci Quarterly, 35(4), 358–360.
  20. 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.
  21. Spickerman, W., Creech, R., & Joyner, R. (1995). On the (3, F) generalizations of the Fibonacci sequence. The Fibonacci Quarterly, 33(1), 9–12.
  22. 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

Comments are closed.