Minimal number of different distances

[Dan Dima]

Take n distinct points in plane / space / d-dimensional space that determine
C(2,n) distances.
Define the sequences a_d (n), n \geq 1 as the minimum number of distinct
values among these distances:
a_2: 0, 1, 1, 2, 2, 3, ...  a_2 (n)   \leq  [n/2].
a_3: 0, 1, 1, 1, 2, ...
a_d (1) = 0, a_d (d+1) = 1, a_{d+1} (n)  \leq  a_d (n)
There is an explicit formula for a_d (n) ?

Best regards,
Dan Dima
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