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%I #25 Mar 28 2019 06:25:56
%S 1,2,5,13,59,285,1987,16057,149430,1551863,17747299,221015026
%N Isomorphism classes of connected 2-in 2-out digraphs, allowing parallel edges but not loops.
%C From _R. J. Mathar_, Mar 15 2019: (Start)
%C The multiset transform (graphs with n>=2 nodes and k>=1 components) is
%C 1
%C 2
%C 5 1
%C 13 2
%C 59 8 1
%C 285 23 2
%C 1987 100 8 1
%C 16057 468 27 2
%C 149430 2943 115 8 1
%C The row sums (Euler transform) are A307180. (End)
%H J. Hu, A. H. MacDonald and B. D. McKay, <a href="https://doi.org/10.1103/PhysRevB.49.15263">Correlations in two-dimensional vortex liquids</a>, Physical Review B, 49, 21 (1994) 15263-15270.
%H R. J. Mathar, <a href="/A306827/a306827.pdf">OEIS A306827</a>
%e For n=3, the a(3)=2 solutions consist of two superimposed directed triangles, one with the triangles oriented consistently and the other with the triangles oriented oppositely.
%Y Cf. A219889 (no multiedges, not necessarily connected), A306892 (loops permitted), A307180 (Euler transf.)
%K nonn,hard
%O 2,2
%A _Brendan McKay_, Mar 12 2019