A306827 Isomorphism classes of connected 2-in 2-out digraphs, allowing parallel edges but not loops.

1, 2, 5, 13, 59, 285, 1987, 16057, 149430, 1551863, 17747299, 221015026

Offset: 2

Author

Brendan McKay, Mar 12 2019

Keywords

• nonn
• hard

Comments

From R. J. Mathar, Mar 15 2019: (Start)

The multiset transform (graphs with n>=2 nodes and k>=1 components) is

1

2

5 1

13 2

59 8 1

285 23 2

1987 100 8 1

16057 468 27 2

149430 2943 115 8 1

The row sums (Euler transform) are A307180. (End)

Examples

			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.
		

Links

• J. Hu, A. H. MacDonald and B. D. McKay, Correlations in two-dimensional vortex liquids, Physical Review B, 49, 21 (1994) 15263-15270.
• R. J. Mathar, OEIS A306827

Crossrefs

Cf. A219889 (no multiedges, not necessarily connected), A306892 (loops permitted), A307180 (Euler transf.)