Geodesic
On a generalization of the Pell sequence
Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 199-213
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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.
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.
DOI : 10.21136/MB.2020.0098-19
Classification : 11B37, 11B39
Keywords: generalized Fibonacci number; generalized Pell number; recurrence sequence 
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Bravo, Jhon J.; Herrera, Jose L.; Luca, Florian. On a generalization of the Pell sequence. Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 199-213. doi: 10.21136/MB.2020.0098-19

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