Journal of Engineering Technology and Applied Sciences

2548-0391

Muhammet KURULAY

10.30931/jetas.994841

Mathematical Sciences

Matematik

De Moivre-Type Identities for the Padovan Numbers

https://orcid.org/0000-0002-0256-1472

Akbıyık

Mücahit

BEYKENT UNIVERSITY

https://orcid.org/0000-0003-1797-674X

Yamaç Akbıyık

Seda

ISTANBUL GELISIM UNIVERSITY

https://orcid.org/0000-0002-9149-7811

Alo

Jeta

BEYKENT UNIVERSITY

12 31 2021

6 3 155 160 09 13 2021 12 24 2021

2016

Journal of Engineering Technology and Applied Sciences

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.

De Moivre-type identity Padovan numbers Perrin numbers quadratic approximation

[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.