On a generalization of the Pell sequence.
| Autor: | Bravo, Jhon J. |
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| Další autoři: | |
| Jazyk: | angličtina |
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| Druh dokumentu: | Non-fiction |
| ISSN: | 0862-7959 |
| Abstrakt: | Abstract: 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: | Katalog Knihovny AV ČR |
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