I'm working on a project that uses strings of integers with the property that the numbers 1 though N are each used twice such that each pair of numbers X are X spaces apart.

For example, in the string:

3 1 1 3 5 7 4 8 6 5 4 2 7 2 6 8

The 1's are 1 space apart, the 2's are 2 spaces apart, the 3's are 3 spaces apart, etc.

I believe I've found the number of unique such strings for the following values of N

N : # of strings

2 : 0

3 : 0

4 : 6

5 : 10

6 : 0

7 : 0

8 : 504

9 : 2656

10 : 0

11 : 0

12 : 455936

I was hoping someone could tell me if someone else has studied these patterns? And if so, could point me in the right direction?