Update lucas_series.py to include another method (#3620)

* Update lucas_series.py

Added another method to calculate lucas_numbers

* Fix pre-commit error

* Update lucas_series.py

* Update lucas_series.py

* Update lucas_series.py

* Update lucas_series.py

maths/lucas_series.py

-# Lucas Sequence Using Recursion
+"""
+https://en.wikipedia.org/wiki/Lucas_number
+"""
 
 
-def recur_luc(n):
+def recursive_lucas_number(n):
     """
-    >>> recur_luc(1)
+    Returns the nth lucas number
+    >>> recursive_lucas_number(1)
     1
-    >>> recur_luc(0)
+    >>> 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
-    return recur_luc(n - 1) + recur_luc(n - 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__":
-    limit = int(input("How many terms to include in Lucas series:"))
-    print("Lucas series:")
-    for i in range(limit):
-        print(recur_luc(i))
+    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)))