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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?

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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

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