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Dergiler / 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
Sayfa
155–160
Yayın Tarihi
2021-12-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Furthermore, we give quadratic approximations for these sequences.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:At this work, we give a method for constructing the Perrin and Padovan sequences and obtain the De Moivre-type identity for Padovan numbers.
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Temel Bulgular & Veri:Also, we define a Padovan sequence with new initial conditions and find some identities between all of these auxiliary sequences.
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Sonuç & Katkı:Furthermore, we give quadratic approximations for these sequences.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (22)

  1. 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.
  2. Sloane, N.J.A., “The on-line encyclopedia integer sequences”, http://oeis.org/. Access date: 10.03.2021.
  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.