

A085549


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


8



1, 2, 4, 10, 28, 97, 359, 1635, 8296, 48432, 316520, 2305104, 18428254, 160384348, 1506613063, 15180782537
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OFFSET

1,2


COMMENTS

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


REFERENCES

B. A. Burton, Minimal triangulations and normal surfaces, Ph.D. thesis, University of Melbourne, 2003.
B. A. Burton, Minimal triangulations and face pairing graphs, preprint, 2003.
B. A. Burton, Enumeration of nonorientable 3manifolds using facepairing graphs and unionfind, Discrete and Computational Geometry, 38 (2007), 527571.


LINKS

Table of n, a(n) for n=1..16.
B. A. Burton, Regina (3manifold topology software).
B. A. Burton, Face pairing graphs and 3manifold enumeration, arXiv:0307382
H. Kleinert, A. Pelster, B. Kastening, M. Bachmann, Recursive graphical construction of Feyman 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
B. Martelli and C. Petronio, Threemanifolds having complexity at most 9, Experiment. Math., Vol. 10 (2001), pp. 207236


PROG

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


CROSSREFS

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


STATUS

approved



