[seqfan] polyominos

[David Newman]

There are lots of sequences in the OEIS related to polyominos constructed
by joining squares at their edges.  Are there sequences counting the number
of shapes where squares may be joined at their corners as well as at their
edges? I've counted such shapes by hand and gotten 1,2,5,19, but this is
not enough information to narrow down the list of possibilities.  I suspect
that someone may have counted these objects before and don't want to put in
the time to write a program to count them if it's already been done.  Does
anyone know if this has been done before?