old_contents: # Lucas Sequence Using Recursion
  
  
  def recur_luc(n):
      """
      >>> recur_luc(1)
      1
      >>> recur_luc(0)
      2
      """
      if n == 1:
          return n
      if n == 0:
          return 2
      return recur_luc(n - 1) + recur_luc(n - 2)
  
  
  if __name__ == "__main__":
      limit = int(input("How many terms to include in Lucas series:"))
      print("Lucas series:")
      for i in range(limit):
          print(recur_luc(i))
  
new_contents: """
  https://en.wikipedia.org/wiki/Lucas_number
  """
  
  
  def recursive_lucas_number(n):
      """
      Returns the nth lucas number
      >>> recursive_lucas_number(1)
      1
      >>> recursive_lucas_number(20)
      15127
      >>> recursive_lucas_number(0)
      2
      >>> recursive_lucas_number(25)
      167761
      >>> recursive_lucas_number(-1.5)
      Traceback (most recent call last):
          ...
      TypeError: recursive_lucas_number accepts only integer arguments.
      """
      if n == 1:
          return n
      if n == 0:
          return 2
      if not isinstance(n, int):
          raise TypeError("recursive_lucas_number accepts only integer arguments.")
  
      return recursive_lucas_number(n - 1) + recursive_lucas_number(n - 2)
  
  
  def dynamic_lucas_number(n: int) -> int:
      """
      Returns the nth lucas number
      >>> dynamic_lucas_number(1)
      1
      >>> dynamic_lucas_number(20)
      15127
      >>> dynamic_lucas_number(0)
      2
      >>> dynamic_lucas_number(25)
      167761
      >>> dynamic_lucas_number(-1.5)
      Traceback (most recent call last):
          ...
      TypeError: dynamic_lucas_number accepts only integer arguments.
      """
      if not isinstance(n, int):
          raise TypeError("dynamic_lucas_number accepts only integer arguments.")
      if n == 0:
          return 2
      if n == 1:
          return 1
      a, b = 2, 1
      for i in range(n):
          a, b = b, a + b
      return a
  
  
  if __name__ == "__main__":
      from doctest import testmod
  
      testmod()
      n = int(input("Enter the number of terms in lucas series:\n").strip())
      n = int(input("Enter the number of terms in lucas series:\n").strip())
      print("Using recursive function to calculate lucas series:")
      print(" ".join(str(recursive_lucas_number(i)) for i in range(n)))
      print("\nUsing dynamic function to calculate lucas series:")
      print(" ".join(str(dynamic_lucas_number(i)) for i in range(n)))
  
subject: Update lucas_series.py to include another method (#3620)