This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355517 #8 Feb 16 2025 08:34:03
%S A355517 1,2,1,4,50,7443,95239971
%N A355517 Number of nonisomorphic systems enumerated by A334254; that is, the number of inequivalent closure operators on a set of n elements where all singletons are closed.
%C A355517 The T_1 axiom states that all singleton sets {x} are closed.
%C A355517 For n>1, this property implies strictness (meaning that the empty set is closed).
%H A355517 Dmitry I. Ignatov, <a href="https://github.com/dimachine/ClosureSeparation/">Supporting iPython code for counting nonequivalent closure systems w.r.t. the T_1 separation axiom</a>, Github repository
%H A355517 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SeparationAxioms.html">Separation Axioms</a>
%H A355517 Wikipedia, <a href="http://en.wikipedia.org/wiki/Separation_axiom">Separation Axiom</a>
%e A355517 a(0) = 1 counts the empty set, while a(1) = 2 counts {{1}} and {{},{1}}.
%e A355517 For a(2) = 1 the closure system is as follows: {{1,2},{1},{2},{}}.
%e A355517 The a(3) = 4 inequivalent set-systems of closed sets are:
%e A355517 {{1,2,3},{1},{2},{3},{}}
%e A355517 {{1,2,3},{1,2},{1},{2},{3},{}}
%e A355517 {{1,2,3},{1,2},{1,3},{1},{2},{3},{}}
%e A355517 {{1,2,3},{1,2},{1,3},{2,3},{1},{2},{3},{}}.
%Y A355517 The number of all closure operators is given in A102896, while A193674 contains the number of all nonisomorphic ones.
%Y A355517 For T_1 closure operators and their strict counterparts, see A334254 and A334255, respectively; the only difference is a(1).
%Y A355517 Cf. A326960, A326961, A326979.
%K A355517 nonn,hard,more
%O A355517 0,2
%A A355517 _Dmitry I. Ignatov_, Jul 05 2022