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 http://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