Hi,
I'd like to count the iterations of a loop nest by evaluating a sum.
Consider the following loop nest:
for (k = 0; k < N; k++)
for (i = k+1; i < N; i++)
for (j = k+1; j <= i; j++)
...
I'd like to count the total number of iterations of that loop nest.
I've used mathematica a bit, and you could solve this problem with
something like this:
Sum[1, {k, 0, N}, {i, k+1, N}, {j, k+1, i-1}]
The result should be in terms of N. For this loop nest the closed
form is:
1 / 6 * (1 + N) * (N^2 - N)
I've been trying to figure out how to do this sort of problem in Sage,
but I have been unsuccessful. Any help would be greatly appreciated.
Thanks,
Patrick
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