What I came up with was 1,673 aunts/uncles (when I started the project). It ended up being 2,184.
Why the difference? Some thoughts:
- The estimate was based on my mother's side of the family only. Now while my father's branch of the family tree is meager in comparison, it does add a few dozen people.
- The estimate was based only on generations 3 through 10. I actually ended up working out to generation 13 (although far from complete).
So - now that I've done the 1st cousins N times removed (8,245 of them) - that ends up being short of the expected 9,760. Why is that?
Two things, I think. First in the estimate going from direct ancestors to aunts/uncles, we KNOW that each of them were married (they're grandparents, after all) whereas there's no guarantee that every child who is an aunt/uncle will also have children (some die early, others never marry, etc.). Another effect is that single-marriage families might have children over a period of 20 years or more, multiple marriage families have a shorter window, which means fewer children per family.
Without looking at every aunt/uncle and removing all the cases where there are no children (code which I could write I suppose), getting an accurate measurement from the aunts/uncles to 1st cousins to estimate the family size for 2nd cousins would be difficult.
In any case, the ratio of 1st cousins to aunt/uncles is 3.8 instead of 5.8 which is essentially an "effective" family size (i.e., counting non-married people in as a family size of zero).
So - I suppose to zeroth-order, the estimate number of 2nd cousins (the C:X,3's on the tree) should be about 31,000 people. Given that I seem to be able to add about 10K people/year, I guess we should expect the next report on this to happen in Spring 2021. :-)