I'm trying to find a recurrence relation for how many full binary trees there are with n nodes. However, once I get to n = 11, it's there's a lot of trees to keep track of. I've written out the cases for $$n \in [1,9] $$ where n is odd but I can't figure out the pattern.
At n=1, I have 1.
n = 3, I have 1
n = 5 : 2 /// n = 7 : 5 /// n = 9 : 14
Basically I took the leaves from the previous nth tree I created and added 2 nodes to each leaf for all possible full binary trees then got rid of duplicates. I.e for n = 7, I took leaves from n = 5, which is 3 and added 2 nodes to each leaf from all the fbts possible when n = 5 (which is 2) and so I end up with 6 fbts, but there's 1 duplicate so I subtract 1 to end up with 5 distinct fbts.
Any help on figuring out the pattern or atleast how many distinct fbts with n nodes?