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A367904
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Number of sets of nonempty subsets of {1..n} with only one possible way to choose a sequence of different vertices of each edge.
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33
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1, 2, 6, 38, 666, 32282, 3965886, 1165884638, 792920124786, 1220537093266802, 4187268805038970806, 31649452354183112810198, 522319168680465054600480906, 18683388426164284818805590810122, 1439689660962836496648920949576152046, 237746858936806624825195458794266076911118
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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The set-system Y = {{1},{1,2},{2,3}} has choices (1,1,2), (1,1,3), (1,2,2), (1,2,3), of which only (1,2,3) has all different elements, so Y is counted under a(3).
The a(0) = 1 through a(2) = 6 set-systems:
{} {} {}
{{1}} {{1}}
{{2}}
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
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MATHEMATICA
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Table[Length[Select[Subsets[Subsets[Range[n]]], Length[Select[Tuples[#], UnsameQ@@#&]]==1&]], {n, 0, 3}]
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CROSSREFS
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The maximal case (n subsets) is A003024.
The version for at least one choice is A367902.
A059201 counts covering T_0 set-systems.
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KEYWORD
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nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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