S

```
"""
A hexagonal number sequence is a sequence of figurate numbers
where the nth hexagonal number hₙ is the number of distinct dots
in a pattern of dots consisting of the outlines of regular
hexagons with sides up to n dots, when the hexagons are overlaid
so that they share one vertex.
Calculates the hexagonal numbers sequence with a formula
hₙ = n(2n-1)
where:
hₙ --> is nth element of the sequence
n --> is the number of element in the sequence
reference-->"Hexagonal number" Wikipedia
<https://en.wikipedia.org/wiki/Hexagonal_number>
"""
def hexagonal_numbers(length: int) -> list[int]:
"""
:param len: max number of elements
:type len: int
:return: Hexagonal numbers as a list
Tests:
>>> hexagonal_numbers(10)
[0, 1, 6, 15, 28, 45, 66, 91, 120, 153]
>>> hexagonal_numbers(5)
[0, 1, 6, 15, 28]
>>> hexagonal_numbers(0)
Traceback (most recent call last):
...
ValueError: Length must be a positive integer.
"""
if length <= 0 or not isinstance(length, int):
raise ValueError("Length must be a positive integer.")
return [n * (2 * n - 1) for n in range(length)]
if __name__ == "__main__":
print(hexagonal_numbers(length=5))
print(hexagonal_numbers(length=10))
```