The *Fibonacci sequence* \(F_n\) is defined by the property that \(F_n = F_{n-1} + F_{n-2}\) for every \(n \ge 2\).

We usually require that \(F_0 = F_1 = 1\).

The sequence begins \(1, 1, 2, 3, 5, 8, 13, 21,\dotsc\)

The numbers in this sequence are called *Fibonacci numbers* and the equation defining the sequence is called the *Fibonacci equation*. The sequence is named after Leonardo Pisano Fibonacci.

The ratio of consecutive Fibonacci numbers tends to the golden ratio, \(\phi\): \[ \lim_{n\to\infty} \frac{F_{n+1}}{F_n} = \phi = \frac{1+\sqrt{5}}{2}. \]