The challenge is that equivalence matrices don't uniquely map to numbers in the sequence: many equivalence matrices can (and do) map to the same number. For instance, every identity matrix, of whatever size, maps to `0`. So I can give *an* example of a matrix for each of the first few terms in the sequence, but I can't give *the* example for each.
What I wonder is (a) how much should that ^^ be explained, or (b) does that ^^ mean that giving a first few examples isn't actually helpful?