きったんの頭_ん中☆

#! /usr/bin/env python3
"""
pe6.py
https://mind.kittttttan.info/py/pe6
"""

def pe6(n=100):
    """
    What is the difference between the sum of the squares and
    the square of the sums?
    """
    """
    s1 = sum([x for x in range(1, n + 1)])
    s2 = sum([x * x for x in range(1, n + 1)])
    return s1*s1 - s2
    
    s1 = n*(n+1)/2
    s2 = n*(n+1)*(2*n+1)/6
    s1*s1 - s2
        = n*(n+1)*(n*(n+1)/4 - (2*n+1)/6)
        = n*(n+1)*(3*n*(n+1) - 2*(2*n+1))/12
        = n*(n+1)*(3*n*n - n - 2)/12
        = n*(n+1)*(n-1)*(3*n+2)/12
    """
    print(n * (n + 1) * (n - 1) * (3 * n + 2) // 12)

if __name__ == "__main__":
    pe6()