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### 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