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On a generalization of the Pell sequence
The Pell sequence is the second order linear recurrence defined by with initial conditions and . In this paper, we investigate a generalization of the Pell sequence called the -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
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