TREE sequence

The TREE sequence is a very fast-growing function arising out of.

Suppose we have a sequence of k- T1, T2 ... with the following properties:


 * 1) Each tree Ti has at most i vertices.
 * 2) No tree is  into any tree following it in the sequence.

states that such a sequence cannot be infinite. Mathematician Harvey Friedman expanded on this by asking the question: what is the maximum length of such a sequence for given values of k?

The length of such a sequence is a function of k dubbed TREE(k). The first two values are TREE(1) = 1 and TREE(2) = 3. The next value, TREE(3) is so large that it surpasses many large combinatorial constants like n(4); it is the subject of extensive research regarding its size. Since TREE(3) > n(4), a very weak lower bound for it is AA(187196)(1) using the Ackermann function.