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 A341471 #41 Feb 27 2021 10:58:47
%S A341471 1,1,3,21,317,9735,583907,66226033,13837055261
%N A341471 Number of antisymmetric, antitransitive relations on n labeled nodes.
%C A341471 An antisymmetric, antitransitive relation is one where xRy implies "not yRx" and xRy and yRz implies "not xRz". All antitransitive relations are irreflexive, so this sequence is counting "anti-equivalence relations".
%C A341471 a(n) < A047656(n).
%C A341471 Idea thanks to Richard Arratia, who saw, verbatim in an editorial, "False equivalences? There were almost too many to count."
%H A341471 Wikipedia, <a href="https://en.wikipedia.org/wiki/Binary_relation#Properties">Binary relation</a>
%e A341471 There are a(3) = 21 antisymmetric, antitransitive relations on n = 3 letters:
%e A341471 - the empty relation,
%e A341471 - all six relations containing only a single pair (x,y) (with x != y),
%e A341471 - all twelve relations {(x1,y1), (x2,y2)} containing exactly two ordered pairs, neither of which is (y1,x1) or (y2,x2), and
%e A341471 - two relations containing three ordered pairs: {(1,2), (2,3), (3,1)} and {(1,3), (3,2), (2,1)}.
%Y A341471 Number of relations on labeled nodes: A000110 (equivalence), A001831 (transitive and antitransitive), A002416 (unrestricted), A006125 (symmetric), A006905 (transitive), A047656 (reflexive and antisymmetric), A083667 (antisymmetric), A341473 (antitransitive).
%K A341471 nonn,more
%O A341471 0,3
%A A341471 _Peter Kagey_, Feb 13 2021
%E A341471 a(6)-a(8) from _Bert Dobbelaere_, Feb 27 2021