Guessing the structure of a finger tree from the number of elements
From first principles, every 2-3 tree is a finger tree viewed from another angle, so you could solve the problem by solving the somewhat easier problem of "What shape are the valid 2-3 trees of size $n$?"

You can also look at many existing finger-tree libraries. The first one created, was, of course, the Haskell one. The function you are looking for is replicate, which takes a value $v$ and size $n$, then creates a finger tree of size $n$ containing $n$ copies of $v$. The real work of replicate is done in applicativeTree, which has individual cases for $n \leq 8$ and recurses for larger $n$.