1500: Triangular Sums

The n^th Triangular number, T(n) = 1 + … + n, is the sum of the first n integers. It is the number of points in a triangular array with n points on side. For example T(4):

   X
  X X
 X X X
X X X X

Write a program to compute the weighted sum of triangular numbers: W(n) = SUM[k = 1…n; k * T(k + 1)]

The first line of input contains a single integer N, (1 ≤ N ≤ 1000) which is the number of datasets that follow. Each dataset consists of a single line of input containing a single integer n, (1 ≤ n ≤300), which is the number of points on a side of the triangle.

For each dataset, output on a single line the dataset number (1 through N), a blank, the value of n for the dataset, a blank, and the weighted sum ,W(n), of triangular numbers for n.

4
3
4
5
10

1 3 45
2 4 105
3 5 210
4 10 2145