How many ancestors do you have?

The Eastman newsletter had an interesting post on the numbers of ancestors we each have. You can find it here. Ten generations back and you have over 1000 direct genetic ancestors (e.g., parents, grandparents, great-grandparents). Twenty generations back and you have over 1 million. Thirty generations and you have over 1 billion. Of course it doubles at each generation.

It made me wonder a few things:

• These numbers assume that each ancestor is unique. In any one generation, the same direct ancestor might appear multiple times. The larger the size of the generation, the more prevalent it is going to be.
• How do these numbers compare to the total population size at the time? Clearly, these number cross, with world population rising (exponentially?) as time goes forward and the size of the generation getting smaller by half. According to one account, the world's population in 1800 was one billion. That was approximately ten generations back (where there would have been about 1000 ancestors). But if you go farther back, you'll have more ancestors than people?
• If your ancestry comes from one cultural group or geographic area to the exclusion of others, how much more prevalent is amount of duplication of ancestors?
• Can genetic testing give us any insights into the numbers of ancestors that are duplicated? At which generation those duplications exist?
• Are there more sophisticated ways to measure or estimate these things mathematically? What other information do you need?

I'd love any insights or pointers to existing scholarly work.