powers of Antisymmetric Signed binary Matrices

[Marc LeBrun]

 > Edwin Clark
 > ...with entries 0,1,or -1 ...
 > BTW I'm not sure that "signed binary" is a well-known concept. I did,
 > however, find reference to "signed bit" representation of integers.

Knuth calls the number system with "trits" -1, 0, +1 "balanced ternary".

But in this context "binary" or "ternary" seems misleading, since here 
these values are actual magnitudes, not the components of a representation.

Why not just say something like

   "Number of nXn matrices whose k-th powers for 0<=k<=n^2 have all 
elements in {0,1}"

or "...{-1,0,+1}" as the case may be?

Writing these sets out explicitly is actually more concise than the "-ary" 
jargon anyway!

Perhaps I missed this: what's the significance of the n^2?

Thanks!