# Java recursive Fibonacci sequence

Please explain this simple code:

```public int fibonacci(int n)  {
if(n == 0)
return 0;
else if(n == 1)
return 1;
else
return fibonacci(n - 1) + fibonacci(n - 2);
}
```

I’m confused with the last line especially because if n = 5 for example, then fibonacci(4) + fibonacci(3) would be called and so on but I don’t understand how this algorithm calculates the value at index 5 by this method. Please explain with a lot of detail!

In fibonacci sequence each item is the sum of the previous two. So, you wrote a recursive algorithm.

So,

```fibonacci(5) = fibonacci(4) + fibonacci(3)

fibonacci(3) = fibonacci(2) + fibonacci(1)

fibonacci(4) = fibonacci(3) + fibonacci(2)

fibonacci(2) = fibonacci(1) + fibonacci(0)
```

Now you already know `fibonacci(1)==1 and fibonacci(0) == 0`. So, you can subsequently calculate the other values.

Now,

```fibonacci(2) = 1+0 = 1
fibonacci(3) = 1+1 = 2
fibonacci(4) = 2+1 = 3
fibonacci(5) = 3+2 = 5
```

And from fibonacci sequence `0,1,1,2,3,5,8,13,21....` we can see that for `5th element` the fibonacci sequence returns `5`.

See here for Recursion Tutorial.