Thanks. So fast! I'm going to try this program right away.

Hi, how did you make these computations? I was planning to implement this feature into the program I'm building, but I'm having trouble to eliminate maps that "seems" different but that are actually the same map (Homeomorphic maps). See this other post: mathoverflow.net/questions/62328/…

I really like this one based on the circle packing theorem, thanks!

Hi Paul, I remember a comment made about this question by Noah Snyder. mathoverflow.net/questions/19240/…. "As far as I know there isn't anyone who is holed up in their attic thinking about only the 4-color theorem, instead there's a lot of people who every time they find a new tool think: hrm, I wonder if this tool would work on the 4-color theorem?" For example check the current reserch of Robin Thomas (people.math.gatech.edu/~thomas)

I think I located one of the pair you were talking about: 1.1.8 and 1.3.4. You are right, these are the same map! I have to review the manual computation of the count of different maps. I still would like to find a formula to count different maps, avoiding to manually calculate them ... also because this is error prone! Thanks!

Hi jc, I added some numerical IDs to the maps. I wasn't able to pinpoint the pairs you were talking about. Can you specify them using the IDs? I just want to be sure we talk about the same pairs of maps.

Actually it matches this one: oeis.org/A163138 (0 does not have to be considered because the map in that case is not regular). But I think 4 terms are just too few and it may be just a coincidence.