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A085549 Number of isomorphism classes of connected 4-regular multigraphs of order n, loops allowed. 9


%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 4-regular multigraphs of order n, loops allowed.

%C Also the number of different potential face pairing graphs for closed 3-manifold 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://regina-normal.github.io/">Regina</a> (3-manifold topology software).

%H B. A. Burton, <a href="https://people.smp.uq.edu.au/BenjaminBurton/papers/2003-thesis.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 3-manifold enumeration</a>, arXiv:math/0307382 [math.GT], 2003.

%H B. A. Burton, <a href="https://people.smp.uq.edu.au/BenjaminBurton/papers/burton07-enumeration.pdf">Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find</a>, Discrete and Computational Geometry, 38 (2007), 527-571.

%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/hep-th/9907168">arXiv:hep-th/9907168</a>, 1999.

%H B. Martelli and C. Petronio, <a href="http://www.emis.de/journals/EM/expmath/volumes/10/10.html">Three-manifolds having complexity at most 9</a>, Experiment. Math., Vol. 10 (2001), pp. 207-236

%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] (* Jean-Fran├žois 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 _Jean-Fran├žois Alcover_, Dec 03 2019

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Last modified July 9 14:41 EDT 2020. Contains 335543 sequences. (Running on oeis4.)