On the Cardinality of the 𝑇₀-Topologies on a Finite Set

Table 6

𝑘	𝑡0(𝑛,𝑘)
5⋅2^𝑛−4	22
5⋅2^𝑛−4+1	4
5⋅2^𝑛−4+2	8
5⋅2^𝑛−4+2^𝑛−𝑖, 9≤𝑖≤𝑛−2	10
5⋅2^𝑛−4+2^𝑛−8	16
5⋅2^𝑛−4+2^𝑛−7	12
5⋅2^𝑛−4+2^𝑛−6	18
5⋅2^𝑛−4+2^𝑛−5	16
5⋅2^𝑛−4+3⋅2^𝑛−𝑖, 6≤𝑖≤𝑛	2
5⋅2^𝑛−4+5⋅2^𝑛−7	6
5⋅2^𝑛−4+5⋅2^𝑛−𝑖, 8≤𝑖≤𝑛	4
3⋅2^𝑛−3	9
3⋅2^𝑛−3+1	2
3⋅2^𝑛−3+2^𝑛−𝑗, 7≤𝑗≤𝑛−1	4
3⋅2^𝑛−3+3⋅2^𝑛−𝑗, 7≤𝑗≤𝑛−1	2
25⋅2^𝑛−6	7
13⋅2^𝑛−5	6
27⋅2^𝑛−6	3
7⋅2^𝑛−4	5
15⋅2^𝑛−5	2
2^𝑛−1	2
2^𝑛−1+2^𝑛−𝑗, 5≤𝑗≤𝑛	2
9⋅2^𝑛−4	3
5⋅2^𝑛−3	2
3⋅2^𝑛−2	1
2^𝑛	1