Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 6 Sayı: 3, 155 - 160, 31.12.2021
https://doi.org/10.30931/jetas.994841

Öz

Kaynakça

  • [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.

De Moivre-Type Identities for the Padovan Numbers

Yıl 2021, Cilt: 6 Sayı: 3, 155 - 160, 31.12.2021
https://doi.org/10.30931/jetas.994841

Öz

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.

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Mücahit Akbıyık 0000-0002-0256-1472

Seda Yamaç Akbıyık 0000-0003-1797-674X

Jeta Alo 0000-0002-9149-7811

Erken Görünüm Tarihi 20 Ocak 2022
Yayımlanma Tarihi 31 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 6 Sayı: 3

Kaynak Göster

APA Akbıyık, M., Yamaç Akbıyık, S., & Alo, J. (2021). De Moivre-Type Identities for the Padovan Numbers. Journal of Engineering Technology and Applied Sciences, 6(3), 155-160. https://doi.org/10.30931/jetas.994841
AMA Akbıyık M, Yamaç Akbıyık S, Alo J. De Moivre-Type Identities for the Padovan Numbers. JETAS. Aralık 2021;6(3):155-160. doi:10.30931/jetas.994841
Chicago Akbıyık, Mücahit, Seda Yamaç Akbıyık, ve Jeta Alo. “De Moivre-Type Identities for the Padovan Numbers”. Journal of Engineering Technology and Applied Sciences 6, sy. 3 (Aralık 2021): 155-60. https://doi.org/10.30931/jetas.994841.
EndNote Akbıyık M, Yamaç Akbıyık S, Alo J (01 Aralık 2021) De Moivre-Type Identities for the Padovan Numbers. Journal of Engineering Technology and Applied Sciences 6 3 155–160.
IEEE M. Akbıyık, S. Yamaç Akbıyık, ve J. Alo, “De Moivre-Type Identities for the Padovan Numbers”, JETAS, c. 6, sy. 3, ss. 155–160, 2021, doi: 10.30931/jetas.994841.
ISNAD Akbıyık, Mücahit vd. “De Moivre-Type Identities for the Padovan Numbers”. Journal of Engineering Technology and Applied Sciences 6/3 (Aralık 2021), 155-160. https://doi.org/10.30931/jetas.994841.
JAMA Akbıyık M, Yamaç Akbıyık S, Alo J. De Moivre-Type Identities for the Padovan Numbers. JETAS. 2021;6:155–160.
MLA Akbıyık, Mücahit vd. “De Moivre-Type Identities for the Padovan Numbers”. Journal of Engineering Technology and Applied Sciences, c. 6, sy. 3, 2021, ss. 155-60, doi:10.30931/jetas.994841.
Vancouver Akbıyık M, Yamaç Akbıyık S, Alo J. De Moivre-Type Identities for the Padovan Numbers. JETAS. 2021;6(3):155-60.