[seqfan] Re: Q: unlabeled 2-regular digraphs

[Richard J. Mathar]

It seems to turn out that A006372 counts the (not necessarily connected)
unlabeled 2-regular digraphs (indegree=outdegree=2) allowing multiedges and loops.
This means in the 4 indices of the products of Riemann tensors, the first 2 indices
(covariant) can be interpreted as the two labels of the outgoing edges and the last
2 indices (contravariant) as the two labels of  incoming edges (or vice versa).
The loops are needed where contractions of indices at the same tensor occur,
which have been printed as R-values with only 2 indices. Isolated vertices with
two loops are double-contractions which have been printed as R without index by Briggs.
I put the associated connected  diagrams into A306892. So extending A306892 and
performing an Euler Transform should also extend A006372.

Richard J. Mathar