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EXAMPLE
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Non-isomorphic representatives of the a(0) = 1 through a(3) = 24 connectedness systems:
{} {{1}} {{1,2}} {{1,2,3}}
{{1},{2}} {{1},{2,3}}
{{2},{1,2}} {{1},{2},{3}}
{{1},{2},{1,2}} {{3},{1,2,3}}
{{1},{3},{2,3}}
{{2,3},{1,2,3}}
{{2},{3},{1,2,3}}
{{1},{2,3},{1,2,3}}
{{1},{2},{3},{2,3}}
{{3},{2,3},{1,2,3}}
{{1},{2},{3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1},{3},{2,3},{1,2,3}}
{{2},{3},{2,3},{1,2,3}}
{{2},{1,3},{2,3},{1,2,3}}
{{3},{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{2,3},{1,2,3}}
{{1},{2},{1,3},{2,3},{1,2,3}}
{{2},{3},{1,3},{2,3},{1,2,3}}
{{3},{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{1,3},{2,3},{1,2,3}}
{{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
{{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
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