# Fibonacci

Non recursive approach

### Equation

$$ f_{n} = \begin{cases} 0 & \text{if } n = 0 \\ 1 & \text{if } n = 1 \\ f_{n-1}+f_{n-2} & \text{if } n >=2 \end{cases} $$

### Manualy calculated examples

n | f0 | f1 | fn |
---|---|---|---|

0 | 0 | 0 | 0 |

1 | 0 | 1 | 1 |

2 | 0 | 1 | 1 |

3 | 1 | 1 | 2 |

4 | 1 | 2 | 3 |

5 | 2 | 3 | 5 |

6 | 3 | 5 | 8 |

7 | 5 | 8 | 13 |

8 | 8 | 3 | 21 |

9 | 13 | 21 | 34 |

10 | 21 | 34 | 55 |

11 | 34 | 55 | 89 |

12 | 55 | 89 | 144 |

13 | 89 | 144 | 233 |

14 | 144 | 233 | 377 |

15 | 233 | 377 | 610 |

16 | 377 | 610 | 987 |

17 | 610 | 987 | 1597 |

18 | 987 | 1597 | 2584 |

19 | 1597 | 2584 | 4181 |

20 | 2584 | 4181 | 6765 |