Yıl: 2021 Cilt: 6 Sayı: 3 Sayfa Aralığı: 155 - 160 Metin Dili: İngilizce DOI: 10.30931/jetas.837921 İndeks Tarihi: 29-07-2022

De Moivre-Type Identities for the Padovan Numbers

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.
Anahtar Kelime: De Moivre-type identity Perrin numbers quadratic approximation Padovan numbers

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [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.
APA AKBIYIK M, YAMAÇ AKBIYIK S, Alo J (2021). De Moivre-Type Identities for the Padovan Numbers. , 155 - 160. 10.30931/jetas.837921
Chicago AKBIYIK Mücahit,YAMAÇ AKBIYIK SEDA,Alo Jeta De Moivre-Type Identities for the Padovan Numbers. (2021): 155 - 160. 10.30931/jetas.837921
MLA AKBIYIK Mücahit,YAMAÇ AKBIYIK SEDA,Alo Jeta De Moivre-Type Identities for the Padovan Numbers. , 2021, ss.155 - 160. 10.30931/jetas.837921
AMA AKBIYIK M,YAMAÇ AKBIYIK S,Alo J De Moivre-Type Identities for the Padovan Numbers. . 2021; 155 - 160. 10.30931/jetas.837921
Vancouver AKBIYIK M,YAMAÇ AKBIYIK S,Alo J De Moivre-Type Identities for the Padovan Numbers. . 2021; 155 - 160. 10.30931/jetas.837921
IEEE AKBIYIK M,YAMAÇ AKBIYIK S,Alo J "De Moivre-Type Identities for the Padovan Numbers." , ss.155 - 160, 2021. 10.30931/jetas.837921
ISNAD AKBIYIK, Mücahit vd. "De Moivre-Type Identities for the Padovan Numbers". (2021), 155-160. https://doi.org/10.30931/jetas.837921
APA AKBIYIK M, YAMAÇ AKBIYIK S, Alo J (2021). De Moivre-Type Identities for the Padovan Numbers. Journal of Engineering Technology and Applied Sciences, 6(3), 155 - 160. 10.30931/jetas.837921
Chicago AKBIYIK Mücahit,YAMAÇ AKBIYIK SEDA,Alo Jeta De Moivre-Type Identities for the Padovan Numbers. Journal of Engineering Technology and Applied Sciences 6, no.3 (2021): 155 - 160. 10.30931/jetas.837921
MLA AKBIYIK Mücahit,YAMAÇ AKBIYIK SEDA,Alo Jeta De Moivre-Type Identities for the Padovan Numbers. Journal of Engineering Technology and Applied Sciences, vol.6, no.3, 2021, ss.155 - 160. 10.30931/jetas.837921
AMA AKBIYIK M,YAMAÇ AKBIYIK S,Alo J De Moivre-Type Identities for the Padovan Numbers. Journal of Engineering Technology and Applied Sciences. 2021; 6(3): 155 - 160. 10.30931/jetas.837921
Vancouver AKBIYIK M,YAMAÇ AKBIYIK S,Alo J De Moivre-Type Identities for the Padovan Numbers. Journal of Engineering Technology and Applied Sciences. 2021; 6(3): 155 - 160. 10.30931/jetas.837921
IEEE AKBIYIK M,YAMAÇ AKBIYIK S,Alo J "De Moivre-Type Identities for the Padovan Numbers." Journal of Engineering Technology and Applied Sciences, 6, ss.155 - 160, 2021. 10.30931/jetas.837921
ISNAD AKBIYIK, Mücahit vd. "De Moivre-Type Identities for the Padovan Numbers". Journal of Engineering Technology and Applied Sciences 6/3 (2021), 155-160. https://doi.org/10.30931/jetas.837921