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EXAMPLE
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Table begins:
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n\k| 1 2 3 4 5 6 7 8 9 10
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1 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ...
2 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ...
3 | 0, 0, 1, 1, 1, 1, 1, 1, 1, 1 ...
4 | 0, 0, 1, 2, 2, 2, 2, 2, 2, 2 ...
5 | 0, 0, 4, 6, 7, 7, 7, 7, 7, 7 ...
6 | 0, 1, 9, 19, 22, 23, 23, 23, 23, 23 ...
7 | 0, 1, 26, 58, 74, 77, 78, 78, 78, 78 ...
8 | 0, 4, 66, 195, 279, 306, 310, 311, 311, 311 ...
9 | 0, 7, 183, 651, 1084, 1255, 1292, 1296, 1297, 1297 ...
10 | 0, 18, 488, 2294, 4554, 5802, 6140, 6194, 6199, 6200 ...
...
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For n=6, we can partition the vertices of C_6 into at most 4 parts in 10 ways such that all these partitions induce distinguishing colorings for C_6 and that all the 10 partitions are non-equivalent.
{ { 1 }, { 2 }, { 3 }, { 4, 5, 6 } }
{ { 1 }, { 2 }, { 3, 4 }, { 5, 6 } }
{ { 1 }, { 2 }, { 3, 4, 6 }, { 5 } }
{ { 1 }, { 2 }, { 3, 5 }, { 4, 6 } }
{ { 1 }, { 2 }, { 3, 6 }, { 4, 5 } }
{ { 1 }, { 2, 3 }, { 4 }, { 5, 6 } }
{ { 1 }, { 2, 3 }, { 4, 6 }, { 5 } }
{ { 1 }, { 2, 4 }, { 3, 6 }, { 5 } }
{ { 1 }, { 2, 4, 6 }, { 3 }, { 5 } }
{ { 1 }, { 2, 5 }, { 3, 6 }, { 4 } }
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