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Well, assuming you are allowed
singles, triples etc, the following ensues:
6 singles (x)
5+4+3+2+1 =15 doubles (sum of singles 1 to x-1)
10+6+3+1 =20 triples (sum of triangles of 1 to x-2)
9+4+1 =14 quartets (sum of squares of 1 to x-3)
6 quintets (when you reach groups of x-1, simply x)
1 sextet (all of them cannot be in any other combinations)
Total it all up and you get 6+15+20+14+6+1 = 62 combinations, no repeats.
(I believe so anyway)
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