TITLE: Sum Notation with restrictions
QUESTION [7 upvotes]: I understand normal sigma notation but what does it mean when we place under a sum the restriction that $i + j + k = n$, for example?  Is this simply $3$ sums in disguise or is it something else?

REPLY [6 votes]: It is basically what you said:

the restriction that i + j + k = n

So if your sum looks like
$$ \sum_{i+j+k=n} g(i,j,k), $$
you sum over all $g(i,j,k)$ where $(i,j,k)$ satisfy the condition. That means you need to find the set of all combinations $\{(i,j,k) | i + j + k = n\}$.