Formula for the $n$th $k$-Generalized Fibonacci-like Number

John Alexis B. Gemino; Alexander J. Balsomo; Geneveve M. Parreño-Lachica; Dave Ryll B. Libre; Marc Raniel A. Nuñeza

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arXiv · 2209.03165

Formula for the $n$th $k$-Generalized Fibonacci-like Number

John Alexis B. Gemino·Alexander J. Balsomo·Geneveve M. Parreño-Lachica·Dave Ryll B. Libre·Marc Raniel A. Nuñeza

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Abstract

In this paper we provided a formula for the $n$th term of the $k$-generalized Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence, having $k$ arbitrary initial terms, where the succeeding terms are obtained by adding its previous $k$ terms. The formula for the $n$th term of the $k$-generalized Fibonacci-like sequence was obtained by observing patterns in the derived formula for the nth term of the Fibonacci-like, Tribonacci-like, and Tetrabonacci-like sequence. The formula for the $k$-generalized Fibonacci sequence was also derived and was used in the process of proving the main result of this paper.

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John Alexis B. Gemino, Alexander J. Balsomo, Geneveve M. Parreño-Lachica, Dave Ryll B. Libre, Marc Raniel A. Nuñeza. 2022-08-27. Formula for the $n$th $k$-Generalized Fibonacci-like Number. https://arxiv.org/abs/2209.03165

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