python https://www.algospot.com/judge/problem/read/DOMINO

Posted 2021-05-09

# -*- coding: utf-8 -*-

#   n0  n1    n2      n3        n4
# ----------------------------------------------
#   0 / 1 2 / 2 3 4 / 3 4 5 6 / 4 5 6 7 8 / ...
# t 0 /   3 /     9 /      18 /        30 / ...
#
# t = sum[n, n+1, n+2, ..., 2n]
#   = (2n까지의 합) - (n-1까지의 합)
#   = (2n+1)*2n/2 - n*(n-1)/2
#   = (2n+1)*n - n*(n-1)/2
#
# S = sum of t(n) for n = [1..N])

print sum([(((n<<1)+1)*n)-((n*(n-1))>>1) for n in xrange(input()+1)])