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.

(According to the [Internet Archive](http://web.archive.org/web/20151014074235/http://legacy.lclark.edu/~miller/langford.html) that page has moved to http://dialectrix.com/langford.html).

Skolem or near Skolem sequences may also be of interest to you.  I have a specialization of this I am studying: see https://mathoverflow.net/questions/61744/has-anyone-seen-this-version-of-ring-toss-combinatorial-object-before .

Gerhard "Yes, Number Theory Is Involved" Paseman, 2011.07.23