## Missouri Journal of Mathematical Sciences

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

#### 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

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