TY - JOUR T1 - De Moivre-Type Identities for the Padovan Numbers AU - Akbıyık, Mücahit AU - Yamaç Akbıyık, Seda AU - Alo, Jeta PY - 2021 DA - December DO - 10.30931/jetas.994841 JF - Journal of Engineering Technology and Applied Sciences JO - JETAS PB - Muhammet KURULAY WT - DergiPark SN - 2548-0391 SP - 155 EP - 160 VL - 6 IS - 3 LA - en AB - 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. KW - De Moivre-type identity KW - Padovan numbers KW - Perrin numbers KW - quadratic approximation CR - [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. CR - [2] Sloane, N.J.A., “The on-line encyclopedia integer sequences” , http://oeis.org/. Access date: 10.03.2021. CR - [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. CR - [4] Yilmaz, N., Taskara, N., “Matrix Sequences in terms of Padovan and Perrin Numbers”, Journal of Applied Mathematics (2013) : 1-7. CR - [5] Yilmaz, N., Taskara, N., “Binomial Transforms of the Padovan and Perrin Matrix Sequences”, Abstract and Applied Analysis (2013) : 1-7. CR - [6] Basin, S. L., “Elementary problems and solutions”, Fibonacci Q. 1 (1963) : 77. CR - [7] Lin, P.Y., “De Moivre-Type Identities for the Tribonacci Numbers”, The Fibonacci Quarterly 26(2) (1988) : 131-134. CR - [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. CR - [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. CR - [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. CR - [11] Cerda-Morales, G., “Quadratic Approximation of Generalized Tribonacci Sequences”, Discussiones Mathematicae General Algebra and Applications 38 (2018) : 227-237. UR - https://doi.org/10.30931/jetas.994841 L1 - https://dergipark.org.tr/tr/download/article-file/1972117 ER -