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%I #27 Mar 21 2023 05:24:27
%S 1,1,2,5,14,50,265,1601,11984,101884
%N Isomorphism classes of connected 2-regular digraphs on n nodes, allowing multiarcs and loops.
%C The graphs are directed, connected and have indegree=outdegree=2 at each node. Multiarcs (connecting two nodes with the same sense of heading) and loops (edges connecting a node to itself) are permitted.
%C The sequence of the same family of graphs which are not necessarily connected is A006372 (the Euler transform of this sequence).
%H R. J. Mathar, <a href="/A306892/a306892.pdf">OEIS A306892</a>
%H R. J. Mathar, <a href="https://arxiv.org/abs/1903.12477">2-regular digraphs of the Lovelock Lagrangian</a>, arXiv:1903.12477 [math.GM] (2019).
%e On n=1 node, the graph is the node with two edges looping back to the node.
%e On n=2 nodes, the graph is either having two pairs of edges (4 edges in total) linking one node to the other, or a loop at each node and two edges (different senses) from one node to the other.
%Y Cf. A306827 (no loops).
%K nonn,more
%O 0,3
%A _R. J. Mathar_, Mar 15 2019
%E a(8) added by _R. J. Mathar_, Apr 08 2019
%E a(9) added by _R. J. Mathar_, Apr 15 2019
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