# Definition:Fibonacci Number/Negative

## Definition

The definition of Fibonacci numbers for negative integers is an extension of the definition for positive integers:

$F_n = \begin{cases} 0 & : n = 0 \\ 1 & : n = 1 \\ F_{n + 2} - F_{n + 1} & : n < 0 \end{cases}$

for all $n \in \Z$.

## Sequence

The sequence of Fibonacci numbers for negative index begins:

$\ldots, 89, -55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0$