Permeability Discrepancy of an Inductor
You can find some calculators to allow you to approximate the inductance of coil wrapped on an open rod. If I plug your numbers into this one, I find 15 turns should be sufficient to yield 40uH with your stated dimensions (it won't let me spread the turns out as much as yours). 



There is a link in the calculator to the equations they've implemented and I suggest you study the equations rather than trusting this (or any other) online calculator. 

The inductance is much less than it would be with a closed magnetic path because the permeability of air is 1/2000 that of your rod. 

A rather thorough treatment of how the effective Al varies with parameters can be had in this document.