

A085549


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


9



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

1,2


COMMENTS

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

Table of n, a(n) for n=1..23.
B. A. Burton, Regina (3manifold topology software).
B. A. Burton, Minimal triangulations and normal surfaces, Ph.D. thesis, University of Melbourne, 2003.
B. A. Burton, Face pairing graphs and 3manifold enumeration, arXiv:math/0307382 [math.GT], 2003.
B. A. Burton, Enumeration of nonorientable 3manifolds using facepairing graphs and unionfind, Discrete and Computational Geometry, 38 (2007), 527571.
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:hepth/9907168, 1999.
B. Martelli and C. Petronio, Threemanifolds having complexity at most 9, Experiment. Math., Vol. 10 (2001), pp. 207236


FORMULA

Inverse Euler transform of A129429.


MATHEMATICA

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


PROG

Can be generated using Regina (see link above), although generation is slow.


CROSSREFS

Column k=4 of A333397.
Cf. A129429, A129417, A005967, A129430, A129432, A129434, A129436, A118560.
Sequence in context: A090594 A188496 A191501 * A022492 A123429 A207018
Adjacent sequences: A085546 A085547 A085548 * A085550 A085551 A085552


KEYWORD

hard,nonn


AUTHOR

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


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 JeanFrançois Alcover, Dec 03 2019


STATUS

approved



