Python/project_euler/problem_06/sol2.py

# -*- coding: utf-8 -*-
"""
Problem:

The sum of the squares of the first ten natural numbers is,
            1^2 + 2^2 + ... + 10^2 = 385

The square of the sum of the first ten natural numbers is,
            (1 + 2 + ... + 10)^2 = 552 = 3025

Hence the difference between the sum of the squares of the first ten natural
numbers and the square of the sum is 3025 − 385 = 2640.

Find the difference between the sum of the squares of the first N natural
numbers and the square of the sum.
"""
from __future__ import print_function

try:
    raw_input  # Python 2
except NameError:
    raw_input = input  # Python 3


def solution(n):
    """Returns the difference between the sum of the squares of the first n
    natural numbers and the square of the sum.
 
    >>> solution(10)
    2640
    >>> solution(15)
    13160
    >>> solution(20)
    41230
    >>> solution(50)
    1582700
    """
    suma = n * (n + 1) / 2
    suma **= 2
    sumb = n * (n + 1) * (2 * n + 1) / 6
    return int(suma - sumb)


if __name__ == "__main__":
    print(solution(int(raw_input().strip())))