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

2,2

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)

Links

Table of n, a(n) for n=2..13.

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

Example

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.

Crossrefs

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

Sequence in context: A075738 A076999 A360507 * A028856 A013497 A260232

Adjacent sequences: A306824 A306825 A306826 * A306828 A306829 A306830

Keyword

nonn,hard

Author

Brendan McKay, Mar 12 2019

Status

approved