# Fibonacci sum for the given number

#### Problem description :

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:

`0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...`

In mathematical terms, the sequence `F(n)`

of Fibonacci numbers is defined by the recurrence relation

`F(n) = F(n-1) + F(n-2)`

, with seed values `F(0) = 0, F(1) = 1, F(2) = 1`

.

**Input :** A number >= 0

**Output :** A Number

#### Logic :

- Cached the already calculated fibonacci numbers (aka dynamic programming).
- If the number is not calculated then call the function again (aka recurssion).

exponential time complexity with this recursive technique, though. a dynamic bottom-up approach?