I am asked to find a recurrence relationship for a sports tournament where a player will win K hundred of dollars based on the number of people in the subtournament he or she wins (so, a subtournament includes a player, their victims, their victims's victims).

Am I correct that pictorially this is a binary tree? And at the base of the tree we have n people (for the total number of contestants) and at the top we have 1 person. So basically the amount of money to be won at any level is the number of its children X 100?

Then do we have the following recurrence for the number of people at each level: a(n) = 2*(a(n-1)) and wouldn't I multiply that by 100 to get the number of $ paid for everyone at that level? But how to find the total dollars paid ... Thanks!