OFFSET
0,2
COMMENTS
The axiom of choice says that, given any set of nonempty sets Y, it is possible to choose a set containing an element from each. The strict version requires this set to have the same cardinality as Y, meaning no element is chosen more than once.
LINKS
Wikipedia, Axiom of choice.
FORMULA
a(n) = 2^2^n - A367902(n). - Christian Sievers, Aug 01 2024
EXAMPLE
The a(2) = 9 sets of sets:
{{}}
{{},{1}}
{{},{2}}
{{},{1,2}}
{{},{1},{2}}
{{},{1},{1,2}}
{{},{2},{1,2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n]]], Select[Tuples[#], UnsameQ@@#&]=={}&]], {n, 0, 3}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 05 2023
EXTENSIONS
a(5)-a(8) from Christian Sievers, Aug 01 2024
STATUS
approved