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%I #26 Dec 21 2020 07:52:25
%S 1,0,0,0,1,6,39,221,1237
%N Number of 2-connected multigraphs with n edges rooted at two noninterchangeable vertices and have no decomposition into parallel components rooted at the two distinguished vertices.
%C Variant of A339123, treating the distinguished points as not interchangeable.
%C Graphs that are 2-connected also have no decomposition into series components, so the graphs enumerated by this sequence are the minimal subset of oriented networks which when combined in series and parallel produce all possible networks with a source and a sink and in which every edge lies on a path between the source and the sink.
%e a(6) = 6, Figures 5 and 6 are A/Z-mirrored images of 1 and 3:
%e .
%e A A A A A A
%e // \ / \ d \ / \ / \ / \
%e // \ /___\ / \ / \ / \ / \
%e o-----o o --- o o-----o o--o--o o-----o o-----o
%e \ / \ / \ / \ / \\ / \ /
%e \ / \ / \ / \ / \\ / q /
%e Z Z Z Z Z Z
%e .
%e Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6
%Y Cf. A338999, A339045, A339123.
%K nonn,more
%O 1,6
%A _Rainer Rosenthal_, Nov 27 2020
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