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%I M1512 #45 Nov 19 2023 01:55:07
%S 2,5,17,71,388,2592,21096,204638,2317172,30024276,437469859,
%T 7067109598,125184509147,2410455693765,50101933643655,
%U 1117669367609605,26629298567576331,674793598023809924,18119844622209998036
%N Number of isomorphism classes of connected 3-regular multigraphs of order 2n, loops allowed.
%C a(n) is the number of maximal cells in the moduli space of tropical curves of genus n+1; see Melody Chan (2012) reference. a(n) is also the number of maximally degenerate stable nodal algebraic curves of genus n+1, up to isomorphism, by the association of a stable nodal curve to its dual graph. - _Harry Richman_, Oct 23 2023
%D A. T. Balaban, Enumeration of Cyclic Graphs, pp. 63-105 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976; see p. 92.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. Brinkmann, N. Van Cleemput, and T. Pisanski, <a href="https://doi.org/10.1016/j.tcs.2012.01.018">Generation of various classes of trivalent graphs</a>, Theor. Comput. Sci. 502 (2013) 16-29, Table 1 column LM.
%H Melody Chan, <a href="http://dx.doi.org/10.2140/ant.2012.6.1133">Combinatorics of the tropical Torelli map</a>, Algebra Number Theory, 6 (2012), 1133-1169.
%H Melody Chan, <a href="https://doi.org/10.1090/noti2360">Moduli Spaces of Curves: Classical and Tropical</a>, Notices Amer. Math. Soc., 68 (2021), 1700-1713.
%H R. de Mello Koch and S. Ramgoolam, <a href="https://doi.org/10.1103/PhysRevD.85.026007">Strings from Feynman graph counting: Without large N</a>, Phys. Rev. D 85 (2012) 026007 (D7).
%H R. J. Mathar, <a href="/A005967/a005967.pdf">Cubic Multigraphs A005967</a>
%H R. J. Mathar, <a href="http://vixra.org/abs/1901.0148">Feynman diagrams of the QED vacuum polarization</a>, vixra:1901.0148 (2019).
%H Brendan McKay, <a href="http://users.cecs.anu.edu.au/~bdm/nauty/">nauty software</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Moduli_of_algebraic_curves">Moduli of algebraic curves</a>.
%F Inverse Euler transform of A129427.
%Y Column k=3 of A333397.
%Y Cf. A129427 (Euler transf.), A000421 (no loops), A085549, A129430, A129432, A129434, A129436.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Checked by _Brendan McKay_, Apr 15 2007
%E Using sequence A129427, terms a(12)-a(16) were computed in GAP by _Ignat Soroko_, Apr 07 2010
%E a(17)-a(19) added by _Andrew Howroyd_, Mar 19 2020
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