De Moivre-Type Identities for the Padovan Numbers

Yıl 2021, Cilt: 6 Sayı: 3, 155 - 160, 31.12.2021

Mücahit Akbıyık , Seda Yamaç Akbıyık , Jeta Alo

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.

Anahtar Kelimeler

De Moivre-type identity , Padovan numbers , Perrin numbers , quadratic approximation

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.