Commun. Korean Math. Soc. 2022; 37(4): 977-988
Online first article September 7, 2022 Printed October 31, 2022
https://doi.org/10.4134/CKMS.c210367
Copyright © The Korean Mathematical Society.
Jhon J. Bravo, Jose L. Herrera
Universidad del Cauca; Universidad del Cauca
The Padovan sequence is the third-order linear recurrence $(\mathcal{P}_n)_{n\geq 0}$ defined by $\mathcal{P}_n=\mathcal{P}_{n-2}+\mathcal{P}_{n-3}$ for all $n\geq 3$ with initial conditions $\mathcal{P}_0=0$ and $\mathcal{P}_1=\mathcal{P}_2=1$. In this paper, we investigate a generalization of the Padovan sequence called the $k$-generalized Padovan sequence which is generated by a linear recurrence sequence of order $k\geq 3$. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.
Keywords: Fibonacci number, generalized Padovan number, recurrence sequence
MSC numbers: 11B37, 11B39
Supported by: The first author was supported in part by Project VRI ID 5385 (Universidad del Cauca). The second author thanks the Universidad del Cauca for support during his Ph.D. studies.
2018; 33(3): 695-704
2017; 32(3): 511-522
2016; 31(3): 447-450
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd