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

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 o...

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Bibliographic Details
Main Authors:	Gemino, John Alexis B, Balsomo, Alexander J, Parreño-Lachica, Geneveve M, Libre, Dave Ryll B, Nuñeza, Marc Raniel A
Format:	Journal Article
Language:	English
Published:	27-08-2022
Subjects:	Mathematics - General Mathematics
Online Access:	Get full text
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Summary:	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.
DOI:	10.48550/arxiv.2209.03165