def 							UpperCamelCase		(			__lowercase		:					Optional[Any]      ):
		'''simple docstring'''




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


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










def     lowercase	(    a = 50 ):



		'''simple docstring'''




		SCREAMING_SNAKE_CASE_				:int				     =						[1] * (length + 1)

		for row_length in range(3     , length + 1 ):
				for block_length in range(3     , row_length + 1 ):
						for block_start in range(row_length - block_length ):
								ways_number[row_length] += ways_number[
								    row_length - block_start - block_length - 1
								]

						ways_number[row_length] += 1

		return ways_number[length]


if __name__ == "__main__":
		print(F'''{solution() = }''')






