A095268 Graphical Partitions - Extend?

[franktaw at netscape.net]

I should have said, if the lead non-zero term is a 1 at an even index, 
the stated equivalence holds.

If the lead non-zero term is at an odd index, there is no convolution 
square root.  If the lead non-zero term is not a perfect square, the 
convolution square root is not integral (or even rational).  If the 
lead term is a square greater than 1, the convolution square root will 
consist of rational numbers; I don't know of any simple way to 
determine whether they will be integers.

Franklin T. Adams-Watters


-----Original Message-----
From: franktaw at netscape.net
 
Second, as I'm sure Paul knows, a sequence has a self-convolution 
square-root iff all the odd-index terms are even. So far, A095268 has a 
strict alternation of parity. Does that continue?