Polyomino Request

[franktaw at netscape.net]

I'm wondering if anybody has a table of polyominos classified by their orbits under permutations.  If not, it should be easy to modify a polyomino generating program to generate such a table.  For example, the entries for pentominos might look like:
 
5 [1^5]
2 [1^5] [1^3,2]
3 [1^5] [1,2^2]
1 [1^5]^2 [1,2^2]^2
1 [1^5] [1^3,2]^2 [1,2^2]^3 [1,4]^2
 
The first line here represents the five asymmetric pentominos, which have all five squares fixed under their only symmetry, the identity.  The last line is the "X" pentomino: the identity fixes all five squares; the horizontal and vertical flips fix one axis and swap one pair; the diagonal flips and the 180 degree rotation fix the central square and pair up the others; and the two 90 degree rotations fix the center and put the other four into a single cycle.
 
My primary interest in this is for the "piled" polycubes I introduced recently, but they are also useful for polyomino counting problems.  For example, the number of two-color polyominos starts:
 
1,2,3,12,54,300,1864,12492
 
which is not in the OEIS.  (This is based on a manually generated table up to n=7.  One can also use the information in this table to generate the number of fixed polyominos of size n, which checks, so I am fairly confident that this is correct.)
 
Needless to say, I would like this table extended as far as I can get it.
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
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