How to walk a volume?

A cube, side size N, I want to walk from the center going out, walking on each shell, each step can only add 1 to one direction. How to get the position index?

Example: N=4, first "shell" is the nut of N=2, 8 element; then the outer shell. with N=6 another shell. It's easy to "see" how it walk on continuously.

Is there an algorithm out there to have the walking position vectors generated automatically?

Thanks.

[Walter Roberson]

Is it permitted to visit any vertex twice? Is it permitted to visit the start vertex of the layer twice?