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Journals / Journal of Engineering Technology and Applied Sciences / 2021 / Cilt: 6 Sayı: 3

De Moivre-Type Identities for the Padovan Numbers

Mücahit Akbıyık(BEYKENT UNIVERSITY)0000-0002-0256-1472
Seda Yamaç Akbıyık(ISTANBUL GELISIM UNIVERSITY)0000-0003-1797-674X
Jeta Alo(BEYKENT UNIVERSITY)0000-0002-9149-7811
Pages
155–160
Publication Date
2021-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we give quadratic approximations for these sequences.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:At this work, we give a method for constructing the Perrin and Padovan sequences and obtain the De Moivre-type identity for Padovan numbers.
📊
Key Findings & Data:Also, we define a Padovan sequence with new initial conditions and find some identities between all of these auxiliary sequences.
💡
Conclusion & Impact:Furthermore, we give quadratic approximations for these sequences.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:De Moivre-type identity · Padovan numbers · Perrin numbers

Abstract

At this work, we give a method for constructing the Perrin and Padovan sequences and obtain the De Moivre-type identity for Padovan numbers. Also, we define a Padovan sequence with new initial conditions and find some identities between all of these auxiliary sequences. Furthermore, we give quadratic approximations for these sequences.

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Cite This Article

Akbıyık, M., Akbıyık, S. Y., Alo, J. (2021). De Moivre-Type Identities for the Padovan Numbers. Journal of Engineering Technology and Applied Sciences, Cilt: 6 Sayı: 3, 155–160. https://doi.org/10.30931/jetas.994841

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References (22)

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  3. Vieira, R. P. M., Alves, F. R. V., Cruz, P. M. M., “Catarino Padovan sequence generalization –a study of matrix and generating function”, Notes on Number Theory and Discrete Mathematics 26(4) (2020): 154-163.
  4. Yilmaz, N., Taskara, N., “Matrix Sequences in terms of Padovan and Perrin Numbers”, Journal of Applied Mathematics (2013): 1-7.
  5. Yilmaz, N., Taskara, N., “Binomial Transforms of the Padovan and Perrin Matrix Sequences”, Abstract and Applied Analysis (2013): 1-7.
  6. Basin, S. L., “Elementary problems and solutions”, Fibonacci Q. 1 (1963): 77.
  7. Lin, P.Y., “De Moivre-Type Identities for the Tribonacci Numbers”, The Fibonacci Quarterly 26(2) (1988): 131-134.
  8. Lin, P.Y., “De Moivre-Type Identities for the Tetranacci Numbers”, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht, 4 (1991): 215-218.
  9. Yamaç Akbıyık, S., Akbıyık, M., “De Moivre-Type Identities for the Pell Numbers”, Turkish Journal of Mathematics and Computer Science 13 (1) (2021): 63-67.
  10. Akbıyık, M., Yamaç Akbıyık, S., “De Moivre-Type Identities for the Jacobsthal Numbers”, Notes on Number Theory and Discrete Mathematics 27 (3) (2021): 95-103.
  11. Cerda-Morales, G., “Quadratic Approximation of Generalized Tribonacci Sequences”, Discussiones Mathematicae General Algebra and Applications 38 (2018): 227-237.
  12. Shannon, A. G., Anderson, P. G., Horadam, A. F., “Properties of Cordonnier, Perrin and Van der Laan numbers”, International Journal of Mathematical Education in Science and Technology 37(7) (2006): 825-831.
  13. Sloane, N.J.A., “The on-line encyclopedia integer sequences”, http://oeis.org/. Access date: 10.03.2021.
  14. Vieira, R. P. M., Alves, F. R. V., Cruz, P. M. M., “Catarino Padovan sequence generalization –a study of matrix and generating function”, Notes on Number Theory and Discrete Mathematics 26(4) (2020): 154-163.
  15. Yilmaz, N., Taskara, N., “Matrix Sequences in terms of Padovan and Perrin Numbers”, Journal of Applied Mathematics (2013): 1-7.
  16. Yilmaz, N., Taskara, N., “Binomial Transforms of the Padovan and Perrin Matrix Sequences”, Abstract and Applied Analysis (2013): 1-7.
  17. Basin, S. L., “Elementary problems and solutions”, Fibonacci Q. 1 (1963): 77.
  18. Lin, P.Y., “De Moivre-Type Identities for the Tribonacci Numbers”, The Fibonacci Quarterly 26(2) (1988): 131-134.
  19. Lin, P.Y., “De Moivre-Type Identities for the Tetranacci Numbers”, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht, 4 (1991): 215-218.
  20. Yamaç Akbıyık, S., Akbıyık, M., “De Moivre-Type Identities for the Pell Numbers”, Turkish Journal of Mathematics and Computer Science 13 (1) (2021): 63-67.
  21. Akbıyık, M., Yamaç Akbıyık, S., “De Moivre-Type Identities for the Jacobsthal Numbers”, Notes on Number Theory and Discrete Mathematics 27 (3) (2021): 95-103.
  22. Cerda-Morales, G., “Quadratic Approximation of Generalized Tribonacci Sequences”, Discussiones Mathematicae General Algebra and Applications 38 (2018): 227-237.