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

1, 2, 4, 10, 28, 97, 359, 1635, 8296, 48432, 316520, 2305104, 18428254, 160384348, 1506613063, 15180782537, 163211097958, 1864251304892, 22540603640086, 287577260214946, 3860595341568062, 54397355465967057, 802684717378090204

Offset: 1

Author

Benjamin A. Burton (bab(AT)debian.org), Jul 04 2003

Keywords

• hard
• nonn

Comments

Also the number of different potential face pairing graphs for closed 3-manifold triangulations.

Computed from A129429 by an inverse Euler transform. - R. J. Mathar, Mar 09 2019

References

• B. A. Burton, Minimal triangulations and face pairing graphs, preprint, 2003.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..40
• B. A. Burton, Regina (3-manifold topology software).
• B. A. Burton, Minimal triangulations and normal surfaces, Ph.D. thesis, University of Melbourne, 2003.
• B. A. Burton, Face pairing graphs and 3-manifold enumeration, arXiv:math/0307382 [math.GT], 2003.
• B. A. Burton, Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find, Discrete and Computational Geometry, 38 (2007), 527-571.
• R. de Mello Koch, S. Ramgoolam, Strings from Feynman graph counting: Without large N, Phys. Rev. D 85 (2012) 026007
• H. Kleinert, A. Pelster, B. Kastening, M. Bachmann, Recursive graphical construction of Feynman diagrams and their multiplicities in Phi^4 and Phi^2*A theory, Phys. Rev. E 62 (2) (2000), 1537 eq (4.20) or arXiv:hep-th/9907168, 1999.
• B. Martelli and C. Petronio, Three-manifolds having complexity at most 9, Experiment. Math., Vol. 10 (2001), pp. 207-236
• R. J. Mathar, Illustrations

Crossrefs

Column k=4 of A333397.

Cf. A129429, A129417, A005967, A129430, A129432, A129434, A129436, A118560.

Programs

Mathematica

A129429 = Cases[Import["https://oeis.org/A129429/b129429.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A129429] (* Jean-François Alcover, Dec 03 2019, updated Mar 17 2020 *)

Formula

Inverse Euler transform of A129429.

Extensions

a(12)-a(16) from Brendan McKay, Apr 15 2007, computed using software at http://users.cecs.anu.edu.au/~bdm/nauty/

Edited by N. J. A. Sloane, Oct 01 2007

a(17)-a(23) from A129429 from Jean-François Alcover, Dec 03 2019