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 A382212 #8 Mar 19 2025 09:04:17
%S A382212 0,0,2,6,168,6700,726360,202827786
%N A382212 Number of labeled Eulerian oriented graphs with n nodes without isolated vertices.
%C A382212 This sequence is similar to A007081 but imposes the restriction that the graphs contain no isolated vertices.
%C A382212 Each graph can be considered to represent a generalized rock-paper-scissors game for which a uniformly random strategy is optimal and no draw can be forced.
%H A382212 Wikipedia, <a href="https://en.wikipedia.org/wiki/Rock_paper_scissors">Rock paper scissors</a>
%e A382212 For n=3, the only solutions are given by the directed cycles (1,2,3) and (1,3,2). Similarly, also n=4 only has directed cycles as solutions.
%e A382212 An example of a solution for n=5 is
%e A382212 1 -> {5}
%e A382212 2 -> {5}
%e A382212 3 -> {4}
%e A382212 4 -> {1,2}
%e A382212 5 -> {3,4}
%e A382212 Disconnected solutions exist only for n >= 6.
%Y A382212 Cf. A007081.
%K A382212 nonn,more
%O A382212 1,3
%A A382212 _Bert Dobbelaere_, Mar 18 2025