Inductor coils, core, and a gap between
If you do the maths on a coil wound on a full core it has this inductance: -

$$L = \dfrac{N^2}{\mathcal{R}}$$

Where R is the reluctance of the core and N is the number of turns. L of course, is inductance.

So, if instead of using the reluctance of the ferrous core you regarded it as two reluctances in parallel (one a tube of air and one a core of ferrite) you would get your answer. 

Reluctances in parallel work just like resistances in parallel so, if the tube of air has 100 times the reluctance of the ferrite core then the net reluctance compared to a full ferrite core might increase by only 1%.

See also my answer to the question coil area versus core area. It seeks to justify the equations.