login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085549 Number of isomorphism classes of connected 4-regular 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..23.

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.

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

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] (* Jean-François 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 Jean-François Alcover, Dec 03 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 07:47 EDT 2020. Contains 334697 sequences. (Running on oeis4.)