A Note On The Generalized k-Fibonacci Sequence

Abstract

In this paper, we present a generalization of well-known k-Fibonacci sequence. Namely, we defined generalized k-Fibonacci sequence. This sequence generalizes others, k-Fibonacci sequence, classical Fibonacci sequence, Pell sequence and Jacobsthal sequence. We establish some of the interesting properties of generalized k-Fibonacci sequence. Also, we obtain a generating function for them.

Keywords

• Generalized k-Fibonacci sequence
• k-Fibonacci sequence
• Fibonacci sequence
• Binet’s formula
• Generating function

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