Combinations of resistor networks? I formulated this question while thinking about resistor networks. Suppose you are given N distinct resistors. How many ways are there to combine them into a resistor network? A resistor network is one of the following: * a single resistor * two resistor networks connected in parallel * two resister networks connected in series The two later cases are commutative and associative. ie A+B = B+A and (X+Y)+Z = X+(Y+Z). Equal networks should only be counted once. By what method can we calculate the number of combinations?

this other question is about identical resistors but it is nearly duplicate

Given $n$ identical resistors $R$, find combinations of series, parallel, and series-parallel arrangements