Sure, I can write a test case generator for the "Folding a Ribbon" problem. This generator will create random datasets adhering to the input constraints specified in the problem statement.

Here's the Python code for the test case generator:

```python
import random

def tcgen():
    test_cases = []
    num_datasets = random.randint(1, 100)  # at most 100 datasets

    for _ in range(num_datasets):
        n = random.randint(1, 60)  # 1 ≤ n ≤ 60
        i = random.randint(1, 2**n)  # 1 ≤ i ≤ 2^n
        j = random.randint(1, 2**n)  # 1 ≤ j ≤ 2^n
        test_cases.append((n, i, j))
    
    # Add the terminating line
    test_cases.append((0, 0, 0))

    return test_cases

# Example usage:
if __name__ == "__main__":
    test_cases = tcgen()
    for n, i, j in test_cases:
        print(n, i, j)
```

**Explanation:**

1. **Number of Datasets**: Randomly choose a number of datasets, up to 100.
2. **Generating Each Dataset**:
    - `n`: Number of folds, randomly chosen between 1 and 60.
    - `i`: Layer index, randomly chosen between 1 and \(2^n\).
    - `j`: Part index after unfolding, randomly chosen between 1 and \(2^n\).
3. **Terminating Line**: Add a terminating line `(0, 0, 0)` to signify the end of input.

This script will generate random inputs that can be used to test the solution to the "Folding a Ribbon" problem. You can run the script to get a new set of test cases each time, ensuring that your solution is robust and handles a variety of inputs.