%I
%S 1,2,4,10,28,97,359,1635,8296,48432,316520,2305104,18428254,160384348,
%T 1506613063,15180782537,163211097958,1864251304892,22540603640086,
%U 287577260214946,3860595341568062,54397355465967057,802684717378090204
%N Number of isomorphism classes of connected 4regular multigraphs of order n, loops allowed.
%C Also the number of different potential face pairing graphs for closed 3manifold triangulations.
%C Computed from A129429 by an inverse Euler transform.  _R. J. Mathar_, Mar 09 2019
%D B. A. Burton, Minimal triangulations and face pairing graphs, preprint, 2003.
%H B. A. Burton, <a href="https://reginanormal.github.io/">Regina</a> (3manifold topology software).
%H B. A. Burton, <a href="https://people.smp.uq.edu.au/BenjaminBurton/papers/2003thesis.html">Minimal triangulations and normal surfaces</a>, Ph.D. thesis, University of Melbourne, 2003.
%H B. A. Burton, <a href="https://arxiv.org/abs/math/0307382">Face pairing graphs and 3manifold enumeration</a>, arXiv:math/0307382 [math.GT], 2003.
%H B. A. Burton, <a href="https://people.smp.uq.edu.au/BenjaminBurton/papers/burton07enumeration.pdf">Enumeration of nonorientable 3manifolds using facepairing graphs and unionfind</a>, Discrete and Computational Geometry, 38 (2007), 527571.
%H H. Kleinert, A. Pelster, B. Kastening, M. Bachmann, <a href="https://doi.org/10.1103/PhysRevE.62.1537">Recursive graphical construction of Feynman diagrams and their multiplicities in Phi^4 and Phi^2*A theory</a>, Phys. Rev. E 62 (2) (2000), 1537 eq (4.20) or <a href="https://arxiv.org/abs/hepth/9907168">arXiv:hepth/9907168</a>, 1999.
%H B. Martelli and C. Petronio, <a href="http://www.emis.de/journals/EM/expmath/volumes/10/10.html">Threemanifolds having complexity at most 9</a>, Experiment. Math., Vol. 10 (2001), pp. 207236
%F Inverse Euler transform of A129429.
%t A129429 = Cases[Import["https://oeis.org/A129429/b129429.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerInvTransform is defined in A022562 *)
%t EulerInvTransform[A129429] (* JeanFrançois Alcover, Dec 03 2019, updated Mar 17 2020 *)
%o Can be generated using Regina (see link above), although generation is slow.
%Y Column k=4 of A333397.
%Y Cf. A129429, A129417, A005967, A129430, A129432, A129434, A129436, A118560.
%K hard,nonn
%O 1,2
%A Benjamin A. Burton (bab(AT)debian.org), Jul 04 2003
%E a(12)a(16) from _Brendan McKay_, Apr 15 2007, computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/
%E Edited by _N. J. A. Sloane_, Oct 01 2007
%E a(17)a(23) from A129429 from _JeanFrançois Alcover_, Dec 03 2019
