What you are describing are known as Langford sequences. An Internet search will give you http://legacy.lclark.edu/~miller/langford.html and other links.
Skolem or near Skolem sequences may also be of interest to you. I have a specialization of this I am studying: see Has anyone seen this version of ring toss (combinatorial object) before? .
Gerhard "Yes, Number Theory Is Involved" Paseman, 2011.07.23