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.
%I A361447 #11 Mar 21 2023 23:08:38 %S A361447 1,2,9,49,338,2744,26025,282419,3463502,47439030,718618117, %T A361447 11937743088,215896959624,4224096594516,88919920910684, %U A361447 2004237153640098,48165411560792500,1229462431057436457,33221743136066636436,947415638925100675208,28436953641282225835143 %N A361447 Number of connected 3-regular (cubic) multigraphs on 2n unlabeled nodes rooted at an unoriented edge (or loop) whose removal does not disconnect the graph, loops allowed. %C A361447 a(0) = 1 by convention. Loops add two to the degree of a node. %C A361447 Instead of a rooted edge, the graph can be considered to have a pair of external legs (or half-edges). The external legs add 1 to the degree of a node, but do not contribute to the connectivity of the graph. %C A361447 The 4-regular version of this sequence is A361135 since removing a single edge from a connected even degree regular graph cannot disconnect the graph. %F A361447 G.f.: B(x) - x*(B(x)^2 + B(x^2))/2 where B(x) is the g.f. of A361412. %e A361447 The illustrations in A352175 by _R. J. Mathar_ show 1, 2, 9, and 49 connected graphs corresponding to the initial terms of this sequence. %Y A361447 Cf. A005967 (unrooted), A129427, A352175, A361135, A361412, A361446, A361448. %K A361447 nonn %O A361447 0,2 %A A361447 _Andrew Howroyd_, Mar 12 2023