## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 13, Issue 2 (2001), 92-102.

### A Representation and Some Properties for $k$-Fibonacci Sequences

Gwang-Yeon Lee, Jin-Soo Kim, and Sang-Gu Lee

#### 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.

#### Article information

**Source**

Missouri J. Math. Sci., Volume 13, Issue 2 (2001), 92-102.

**Dates**

First available in Project Euclid: 5 October 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.mjms/1570240959

**Digital Object Identifier**

doi:10.35834/2001/1302092

**Mathematical Reviews number (MathSciNet)**

MR1825067

**Zentralblatt MATH identifier**

1028.11011

#### Citation

Lee, Gwang-Yeon; Kim, Jin-Soo; Lee, Sang-Gu. A Representation and Some Properties for $k$-Fibonacci Sequences. Missouri J. Math. Sci. 13 (2001), no. 2, 92--102. doi:10.35834/2001/1302092. https://projecteuclid.org/euclid.mjms/1570240959