I have written a small program that can automatically generate false counts according to some user-defined constraints. It will be able to "rediscover" classics such as the Elmsley or the Jordan count, but also provide hundreds of new counts that would be not so easy to find by "manual" search.
The program is free (GPL'ed) and comes with source code as well as Windows binaries. If interested you can download it from here:
Thanks and looking forward to your comments!
P.S. To moderators: I've had a hard time deciding which was the best forum to post this, hope I've got it right!