A306827 - OEIS

%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