I'm not sure what this is, but I found it floating around on my computer. It seems to be doing some sort of permutation-like logic.

logic.txt

It seems to be following some permutation-like math:

trees[2] = trees[0]*trees[1] + trees[1]*trees[0]
trees[3] = trees[0]*trees[2] + trees[1]*trees[1] + trees[2]*trees[0]
trees[4] = trees[0]*trees[3] + trees[1]*trees[2] + trees[2]*trees[1] + trees[3]*trees[0]

etc.

I would love to know why it is doing this, but alas, I cannot remember.

treeProblem.lua

-- Interesting metatable implementation for a problem I had on some final or other, but we had to implement it in Java :[

trees = { [0] = 1, [1] = 1 }

setmetatable(trees, {
  __index = function(table, i)
              local sum = 0
              for j = 0, i - 1 do
                sum = sum + table[j]  * table[i - 1 - j]
              end
              
              table[i] = sum
              return sum
            end })