Let’s say you have a system where elementary components can be combined from 0-1 times with each other. E.g.:
If you only have component A, you have 1 possibility: A.
If you have components A and B, you get: A, B, A+B for a total of 3 possibilities.
A, B, C: A, B, C, AB, AC, BC, ABC = 7 possibilities
A, B, C, D: A, B, C, D, AB, AC, AD, BC, BD, CD, BCD, ACD, ABD, ABC, ABCD = 15 possibilities.
Is there a formula that allows one to calculate how many possibilities exist for each number of components?