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EXAMPLE
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Table begins:
=================================================================
n/k | 1 2 3 4 5 6 7 8 9 10
------+----------------------------------------------------------
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, 0, 0, 0, 0, 0, 0, 0, 0, ...
4 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
5 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
6 | 0, 0, 4, 6, 6, 6, 6, 6, 6, 6, ...
7 | 0, 1, 13, 30, 34, 34, 34, 34, 34, 34, ...
8 | 0, 2, 45, 127, 176, 185, 185, 185, 185, 185, ...
9 | 0, 7, 144, 532, 871, 996, 1011, 1011, 1011, 1011, ...
10 | 0, 12, 416, 1988, 3982, 5026, 5280, 5304, 5304, 5304, ...
...
For n=7, we can partition the vertices of the cycle C_7 with at most 3 parts, in 13 ways, such that all these partitions are distinguishing for C_7 and that all the 13 partitions are non-equivalent. The partitions are as follows:
{ { 1 }, { 2, 3 }, { 4, 5, 6, 7 } },
{ { 1 }, { 2, 3, 4, 6 }, { 5, 7 } },
{ { 1 }, { 2, 3, 4, 7 }, { 5, 6 } },
{ { 1 }, { 2, 3, 5, 6 }, { 4, 7 } },
{ { 1 }, { 2, 3, 5, 7 }, { 4, 6 } },
{ { 1 }, { 2, 3, 6 }, { 4, 5, 7 } },
{ { 1 }, { 2, 3, 7 }, { 4, 5, 6 } },
{ { 1 }, { 2, 4, 5, 6 }, { 3, 7 } },
{ { 1 }, { 2, 4, 7 }, { 3, 5, 6 } },
{ { 1, 2 }, { 3, 4, 6 }, { 5, 7 } },
{ { 1, 2 }, { 3, 5, 6 }, { 4, 7 } },
{ { 1, 2, 4 }, { 3, 6 }, { 5, 7 } },
{ { 1, 2, 3, 5 }, { 4, 6, 7 } }.
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