```python
def bracket_seed_order(count: int) -> list:
    if (
        isinstance(count, bool)
        or not isinstance(count, int)
        or count < 2
        or count & (count - 1) != 0
    ):
        raise ValueError("count must be a power of two, at least 2")
    
    sheet = [1]
    while len(sheet) < count:
        sheet = [s for pair in sheet for s in [pair, count + 1 - pair]]
    return sheet
```