On a generalization of the Pell sequence
| Autor: | Jhon J. Bravo, Jose L. Herrera, Florian Luca |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Mathematica Bohemica, Vol 146, Iss 2, Pp 199-213 (2021) |
| Druh dokumentu: | article |
| ISSN: | 0862-7959 2464-7136 |
| DOI: | 10.21136/MB.2020.0098-19 |
| Popis: | The Pell sequence $(P_n)_{n=0}^{\infty}$ is the second order linear recurrence defined by $P_n=2P_{n-1}+P_{n-2}$ with initial conditions $P_0=0$ and $P_1=1$. In this paper, we investigate a generalization of the Pell sequence called the $k$-generalized Pell sequence which is generated by a recurrence relation of a higher order. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences. Some interesting identities involving the Fibonacci and generalized Pell numbers are also deduced. |
| Databáze: | Directory of Open Access Journals |
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