Calculate Jacobsthal Number

### Problem Statement  
The Jacobsthal numbers are a sequence of integers defined by the recurrence relation:  

\[
J(n) = \begin{cases}  
0 & \text{if } n = 0, \\  
1 & \text{if } n = 1, \\  
J(n-1) + 2 \cdot J(n-2) & \text{if } n > 1.  
\end{cases}  
\]  

Write a function `jacobsthal_num(n)` that computes the nth Jacobsthal number.  

### Example Usage  
```python [main.nopy]
jacobsthal_num(0)  # Output: 0
jacobsthal_num(1)  # Output: 1
jacobsthal_num(5)  # Output: 11
jacobsthal_num(10) # Output: 341
```

### Constraints  
- The input `n` will be a non-negative integer.  
- The function should be efficient for values of `n` up to 20.
def jacobsthal_num(n):
    """
    Calculate the nth Jacobsthal number.

    Args:
        n (int): The index of the Jacobsthal number to compute.

    Returns:
        int: The nth Jacobsthal number.
    """
    # Implement the function logic here
    pass
Intermediate recursionmath
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