2g+1

actually, it should be 2^g+1-2. That's the total number of ancestors. 2g+1 has a nicer ring to it though. And the punchline is still just as funny. Plus maybe I was kinda drunk and didn't quite do the math right. Whatever, 2g+1 is way better than 2^(g+1)-2. And you can't really write that in URL form

anywhoo . . . 2^g = the number of folks in that generation

1 generation back = your parents
you have 2 parents
2¹=2
2 parents

2 generations back = your grandparents
you have 4 grandparents
2²=4
4 grandparents

3 generations back = your great-grandparents
you have 8 great-grandparents
2³=8
8 great-grandparents

4 generations back = your great-great-grandparents
you have 16 great-great-grandparents
2⁴=16
16 great-great-grandparents

basically, every generation you go back has double the number of ancestors in it as does the generation before. It starts out manageable, but pretty soon gets completely out of control

10 generations back = your 8x great-grandparents
you may not know this offhand, but you have 1024 8x great-grandparents
2¹⁰=1024
1024 8x great-grandparents

16 generations back = your 14x great-grandparents
2¹⁶=65,536
that's a lot of 14x great-grandparents

the punchline is you actually have far fewer ancestors than that because you're inbred. Don't be too insulted though, everybody is. Do the math. Let's use that 2^g formula and see how many grandparents you'd have if you weren't inbred. There might not be any duplicate grandparents in the first few generations, but go back a few hundred years and guarantee that your ancestors were marrying their cousins. Again and again and again and again

going back 2000 years with an average of 33 years per generation = just over 60 generations

60 generation back = your 58x great-grandparents
2⁶⁰= more than a quintillion
you don't have more than a quintillion 58x great-grandparents

you don't even know what a quintillion is. That's because you're inbred and not very good at math, ha ha ha. But seriously, you're inbred. At the moment there are around 7 billion people on the planet. If you weren't inbred, you'd have more 31x great-grandparents than that. 33 generations is around 1000 years ago. But there weren't even 7 billion people on the planet a thousand years ago, only a few hundred million. Do the math, make a graph, whatever it takes for you to come to terms with the fact that you are severely inbred

so that is 2^g. 2^g+1-2 = all your ancestors including the ones in that generation

1 generation back = your parents
2¹⁺¹-2
2²-2
4-2=2
2 parents

2 generation back = your grandparents
2²⁺¹-2
2³-2
8-2=6
6 ancestors total (2 parents + 4 grandparents)

3 generation back = your great-grandparents
2³⁺¹-2
2⁴-2
16-2=14
14 ancestors total (2 parents + 4 grandparents + 8 great-grandparents)

10 generation back = your 8x great-grandparents
2¹⁰⁺¹-2
2¹¹-2
2048-2=2046
2046 ancestors total (2 parents + 4 grandparents + 8 great-grandparents ... +1024 8x great-grandparents)

of course, you don't actually have 2046 ancestors 10 generations back because you're inbred