cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A339205 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.

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%I A339205 #26 Dec 21 2020 07:52:25
%S A339205 1,0,0,0,1,6,39,221,1237
%N A339205 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 A339205 Variant of A339123, treating the distinguished points as not interchangeable.
%C A339205 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 A339205 a(6) = 6, Figures 5 and 6 are A/Z-mirrored images of 1 and 3:
%e A339205 .
%e A339205       A          A          A          A          A          A
%e A339205     // \        / \        d \        / \        / \        / \
%e A339205    //   \      /___\      /   \      /   \      /   \      /   \
%e A339205    o-----o    o --- o    o-----o    o--o--o    o-----o    o-----o
%e A339205     \   /      \   /      \   /      \   /     \\   /      \   /
%e A339205      \ /        \ /        \ /        \ /       \\ /        q /
%e A339205       Z          Z          Z          Z          Z          Z
%e A339205 .
%e A339205     Fig. 1     Fig. 2     Fig. 3     Fig. 4     Fig. 5    Fig. 6
%Y A339205 Cf. A338999, A339045, A339123.
%K A339205 nonn,more
%O A339205 1,6
%A A339205 _Rainer Rosenthal_, Nov 27 2020