### On Some Identities and Generating Functions for Generalized k-Fibonacci Sequence

#### Abstract

In this article we study a new generalized k-Fibonacci sequence, with initial conditions and which is generated by the recurrence relationand . The main aim of the paper is to present the identities of the generalized k-Fibonacci sequence as well as Binet’s formula and generating functions for the generalized k-Fibonacci sequence. The main results of this paper can be proved by Binet formula method and by induction method.

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**MAYFEB Journal of Mathematics**

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