


from ..utils import DummyObject, requires_backends







class  snake_case_     (metaclass=lowerCamelCase_   ):
					UpperCAmelCase__      :					Optional[Any]					   =    ['''torch''', '''torchsde''']
					def __init__(   self     :Optional[int]    ,*__snake_case     :Optional[int]    ,**__snake_case     :Optional[int]   )      ->					Dict:
												requires_backends(self    ,['torch', 'torchsde']   )
					@classmethod
					def 				lowerCamelCase__(   cls     :Dict    ,*__snake_case     :Union[str, Any]    ,**__snake_case     :Union[str, Any]   )      ->					Tuple:
												requires_backends(cls    ,['torch', 'torchsde']   )



					@classmethod
					def 				lowerCamelCase__(   cls     :Any    ,*__snake_case     :List[Any]    ,**__snake_case     :Any   )      ->					Dict:
												requires_backends(cls    ,['torch', 'torchsde']   )








def 							__lowercase     (				__lowerCAmelCase							:       int     ):

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


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




