[A058387] Series-Parallel Confusion

[Gordon Royle]

I am confused about  A058387

http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A058387

which lists the numbers of series-parallel networks on n unlabelled edges
with no multiple edges.

According to this there are

0 on 0 edges	
1 on 1 edge	(x---x)
1 on 2 edges	(x---x---x)

2 on 3 edges..

But according to the definition of series-parallel with which I am familiar
we should have 3 here - a path of length 3, a 3-star and a triangle.

Can anyone shed any light here? Is "network" simply a synonym for "graph"
(or "connected graph")?

Is there a sequence of "simple series-parallel graphs" by number of vertices..

(I get 1,1,2,5,15,54,227... and want to make sure my program is correct).
 

Cheers

gordon
-- 
Dr. Gordon F Royle, http://www.cs.uwa.edu.au/~gordon, gordon at cs.uwa.edu.au
--