


'''simple docstring'''
def 			a_							(  UpperCamelCase_   ):
							if not isinstance(UpperCamelCase_	,     UpperCamelCase_   ):
														raise TypeError("recursive_lucas_number accepts only integer arguments."   )
							if n_th_number == 0:
														return 2
							if n_th_number == 1:
														return 1

							return recursive_lucas_number(n_th_number - 1   ) + recursive_lucas_number(
							    n_th_number - 2   )







def 			a_							(  UpperCamelCase_   ):
							if not isinstance(UpperCamelCase_	,     UpperCamelCase_   ):
														raise TypeError("dynamic_lucas_number accepts only integer arguments."   )
							A_						,				A_ 						=		2, 1
							for _ in range(UpperCamelCase_   ):
														A_						,				A_ 						=		b, a + b
							return a


if __name__ == "__main__":
							from doctest import testmod

							testmod()
							__SCREAMING_SNAKE_CASE				:							Any		       =		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)))









'''simple docstring'''
def 			a_							(  UpperCamelCase_   ):
							if not isinstance(UpperCamelCase_	,     UpperCamelCase_   ):
														A_ 						=		f"Input value of [number={number}] must be an integer"
														raise TypeError(UpperCamelCase_   )
							if number < 0 or number % 2 == 1:
														return False
							A_ 						=		int(number**0.5   )
							return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
							import doctest

							doctest.testmod()





