Set Equality Counts

Description

It is impossible for sets of certain sizes to have certain total numbers of equalities. For example, a set of 3 items can not have 2 equalities or by the transitive property the third pair must also be equal.

For each number between 1 and 30, print each possible number of equalites separated by spaces, in ascending order and including 0. Each set of numbers should be on it’s own line.