[seqfan] Request help to corroborate calculations

[David Newman]

The notion of nilpotent groups of class n has a long history, as
does the study of their growth. Most of the results are very rough
asymptotic estimates. There is some work of M. Stoll on the finer
properties of these growth functions.
Does anyone out there know if the number of elements of length k for
the free nilpotent group of class n generated by 2 elements has
beencalculated?  If so, where can I find it.

 Another interesting question
concerns the growth of the positive semigroup in the free nilpotent
group, ie the set of elements that can be expressed as products using
the generators but not their inverses.

Would anyone be interested in
corroborating our calculations for semigroups on 2 generators in nilpotent
groups of class 2,3,4,5?"