Geodesic
Periodicity of residues of the number of finite labeled $T_0$-topologies
Zapiski Nauchnykh Seminarov POMI, Modules and algebraic groups, Tome 114 (1982), pp. 32-36

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Let $T_0(n)$ be the number of labeled topologies on points satisfying the $T_0$ separation axiom. It is proved that for any prime $p$ the sequence of residue classes $T_0(n)\mod p$ is periodic with period length $p-1$. 
@article{ZNSL_1982_114_a3,
     author = {Z. I. Borevich},
     title = {Periodicity of residues of the number of finite labeled $T_0$-topologies},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {32--36},
     publisher = {mathdoc},
     volume = {114},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_114_a3/}
}
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Z. I. Borevich. Periodicity of residues of the number of finite labeled $T_0$-topologies. Zapiski Nauchnykh Seminarov POMI, Modules and algebraic groups, Tome 114 (1982), pp. 32-36. http://geodesic.mathdoc.fr/item/ZNSL_1982_114_a3/