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Spring 2001 A Representation and Some Properties for $k$-Fibonacci Sequences
Gwang-Yeon Lee, Jin-Soo Kim, Sang-Gu Lee
Missouri J. Math. Sci. 13(2): 92-102 (Spring 2001). DOI: 10.35834/2001/1302092

Abstract

The $k$-Fibonacci sequence $\{g_n^{(k)}\}$ is defined as: $$ g_1^{(k)}=\ldots=g_{k-2}^{(k)}=0,\;\;g_{k-1}^{(k)}=g_{k}^{(k)}=1 $$ and for $n>k\ge 2$, $$ g_n^{(k)}=g_{n-1}^{(k)}+g_{n-2}^{(k)}+\cdots+g_{n-k}^{(k)}. $$ In this paper, we give a combinatorial representation of $g_n^{(k)}$ and give some properties for $k$-Fibonacci sequence.

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Gwang-Yeon Lee. Jin-Soo Kim. Sang-Gu Lee. "A Representation and Some Properties for $k$-Fibonacci Sequences." Missouri J. Math. Sci. 13 (2) 92 - 102, Spring 2001. https://doi.org/10.35834/2001/1302092

Information

Published: Spring 2001
First available in Project Euclid: 5 October 2019

zbMATH: 1028.11011
MathSciNet: MR1825067
Digital Object Identifier: 10.35834/2001/1302092

Rights: Copyright © 2001 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.13 • No. 2 • Spring 2001
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