cp's OEIS Frontend

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

%I A085549 #46 Mar 07 2023 14:26:52
%S A085549 1,2,4,10,28,97,359,1635,8296,48432,316520,2305104,18428254,160384348,
%T A085549 1506613063,15180782537,163211097958,1864251304892,22540603640086,
%U A085549 287577260214946,3860595341568062,54397355465967057,802684717378090204
%N A085549 Number of isomorphism classes of connected 4-regular multigraphs of order n, loops allowed.
%C A085549 Also the number of different potential face pairing graphs for closed 3-manifold triangulations.
%C A085549 Computed from A129429 by an inverse Euler transform. - _R. J. Mathar_, Mar 09 2019
%D A085549 B. A. Burton, Minimal triangulations and face pairing graphs, preprint, 2003.
%H A085549 Andrew Howroyd, <a href="/A085549/b085549.txt">Table of n, a(n) for n = 1..40</a>
%H A085549 B. A. Burton, <a href="https://regina-normal.github.io/">Regina</a> (3-manifold topology software).
%H A085549 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 A085549 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 A085549 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 A085549 R. de Mello Koch, 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
%H A085549 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 A085549 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
%H A085549 R. J. Mathar, <a href="/A085549/a085549.pdf">Illustrations</a>
%F A085549 Inverse Euler transform of A129429.
%t A085549 A129429 = Cases[Import["https://oeis.org/A129429/b129429.txt", "Table"], {_, _}][[All, 2]];
%t A085549 (* EulerInvTransform is defined in A022562 *)
%t A085549 EulerInvTransform[A129429] (* Jean-François Alcover, Dec 03 2019, updated Mar 17 2020 *)
%o A085549 Can be generated using Regina (see link above), although generation is slow.
%Y A085549 Column k=4 of A333397.
%Y A085549 Cf. A129429, A129417, A005967, A129430, A129432, A129434, A129436, A118560.
%K A085549 hard,nonn
%O A085549 1,2
%A A085549 Benjamin A. Burton (bab(AT)debian.org), Jul 04 2003
%E A085549 a(12)-a(16) from _Brendan McKay_, Apr 15 2007, computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/
%E A085549 Edited by _N. J. A. Sloane_, Oct 01 2007
%E A085549 a(17)-a(23) from A129429 from _Jean-François Alcover_, Dec 03 2019