I'm looking for a way of generating all permutations of three digits (actually xyz) that sum to the same value.

For example:

n = 1:

0 0 0

n = 2:

0 0 1
0 1 0
1 0 0

n = 3:

0 1 1
1 0 1
1 1 0
0 0 2
0 2 0
2 0 0

n = 4:

1 1 2
...

Ideally I need a way of mapping indices to the three digits in a unique way such that I can take an index up to the associated triangle number n * (n + 1) / 2 and find the same three indices every time.

Can anyone point me in the right direction? It's quite some time since I've worked with sequences and I'm a little rusty.