The problem of common ancestors of a generation
A few months ago when I was doing my family tree I had a doubt about the common ancestors. One of the branches of the family data records went back to the seventeenth century (around 1650), specifically the eleventh generation. Based on this I asked myself the following question: how many common relatives of the eleventh generation did I have? To get the result I thought if the first generation we have 2 parents, the second 4 grandparents, the third 8 great-grandparents, the fourth 16 great-great-grandparents and so on. The number of members of each generation is double the previous one, it follows a serial pattern expressed with the equation: $Y = 2^n$, where Y: is the number of members of each generation n: is the number of the generation, $n \in N$. ...