I wonder it would be useful to have a function that given a basis element number x returns the [n, l, m] tuple of the basis. Conversely, have a function that given n, l, m returns the basis element number x. It would be useful and a good place to point the "limitations" of equations presented in Merlet's papers/thesis and make the link with Ozarslan's Figure in the Appendix. 

I believe this would help a lot and clear much of the confusion we had several weeks ago.