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