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