  In this paper, we study the linear space of all two-sided generalized
Fibonacci sequences $\{F_n\}_{n \in \mathbb{Z}}$ that satisfy the recurrence
equation of order $k$: $F_n = F_{n-1} + F_{n-2} + \dots + F_{n-k}$. We give two
types of explicit formula, one is based on generalized binomial coefficients
and the other based on generalized multinomial coefficients.
