






def 		lowercase__  (				_UpperCamelCase) ->			list[int]:
      """simple docstring"""

      if length <= 0 or not isinstance(_UpperCamelCase       ,							_UpperCamelCase):
            raise ValueError('Length must be a positive integer.')
      return [n * (2 * n - 1) for n in range(_UpperCamelCase)]


if __name__ == "__main__":
       print(hexagonal_numbers(length=5))
       print(hexagonal_numbers(length=10))











def 		lowercase__  (				_UpperCamelCase       ,							_UpperCamelCase) ->			bool:
      """simple docstring"""

      return numa ^ numa < 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()



