On the other hand, if you don't require every ancestor to be "unique", that is, not relatives by ancestry, but just want to know the number of unique persons who are ancestors, my simple formula isn't very helpful. If cousins marry and produce a grandchild, that grandchild has 2**3 - 2 great-grandparents instead of 2**3.

Given the propensity of people to stay near where they were born and also the propensity of people to marry within social circles, the "expectation" of the number of generations back for every ancestor being unique is probably quite small.

2**15 = 32,768, 15*20 years/generation = 300 years. So 300 years ago, if your community of eligible ancestors was 32,768 or more, each one could be unique. I guess that's not unreasonable depending where they lived, but it doesn't seem likely.

2**20 = 1,048,576, 20*20 years/generation = 400 years. It seems unlikely to me that your community of eligible ancestors 400 years ago would be over 1 million.

Anyway, that's my uneducated guess.