






def     a_   (__A      )				->						list[int]:



					"""simple docstring"""

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


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













from __future__ import annotations







def     a_   (__A      )				->						int:



					"""simple docstring"""
					__a					:						List[Any]      =					len(__A      ) // 2

					# choose the middle 3 elements
					__a					:						Any      =					lst[m - 1 : m + 2]

					# if middle element is peak
					if three[1] > three[0] and three[1] > three[2]:
										return three[1]

					# if increasing, recurse on right
					elif three[0] < three[2]:
										if len(lst[:m]      ) == 2:
															m -= 1
										return peak(lst[m:]      )

					# decreasing
					else:
										if len(lst[:m]      ) == 2:
															m += 1
										return peak(lst[:m]      )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





