As a part of my first course in graph theory, we are to decide how many non-isomorphic unlabeled trees of order 18 there are. I am not sure how to proceed with this without brute forcing my way and drawing all the 18 non-isomorphic trees. How can I make this problem easier, without having to count all the possible trees?
I am aware of a complicated formula for the number of trees with of order $n$, but I do not think the goal of this assignment is to derive or use the formula, since it involves advanced methods not taught at this level (the generating function for the sequence is well above the level of this course).