# Fibonacci sequence

The numbers satisfying: $LaTeX: F_{n+2} = F_{n+1} + F_n$, with initial conditions $LaTeX: F_0 = F_1 = 1$. As shown in the following table, the fibonacci sequence grows rapidly after $LaTeX: N=10$, and $LaTeX: F_N$ becomes astronomical for $LaTeX: N > 50$,

```         N    F_N
==============
0      1
1      1
2      2
3      3
4      5
5      8
6     13
7     21
8     34
9     55
10     89
20  10946
50    2.0E10
100    5.7E20
==============
```

Named after the 13th century mathematician who discovered it, this sequence has many interesting properties, notably for an optimal univariate optimization strategy, called fibonacci search.