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A005967 Number of isomorphism classes of connected 3-regular multigraphs of order 2n, loops allowed.
(Formerly M1512)
11
2, 5, 17, 71, 388, 2592, 21096, 204638, 2317172, 30024276, 437469859, 7067109598, 125184509147, 2410455693765, 50101933643655, 1117669367609605, 26629298567576331, 674793598023809924, 18119844622209998036 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

A. T. Balaban, Enumeration of Cyclic Graphs, pp. 63-105 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976; see p. 92.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..19.

G. Brinkmann, N. Van Cleemput, T. Pisanski, Generation of various classes of trivalent graphs, Theor. Comput. Sci. 502 (2013) 16-29, Table 1 column LM.

R. de Mello Koch, S. Ramgoolam, Strings from Feynman graph counting: Without large N, Phys. Rev. D 85 (2012) 026007 (D7).

R. J. Mathar, Cubic Multigraphs A005967

R. J. Mathar, Feynman diagrams of the QED vacuum polarization, vixra:1901.0148 (2019).

Brendan McKay, nauty software

FORMULA

Inverse Euler transform of A129427.

CROSSREFS

Column k=3 of A333397.

Cf. A129427 (Euler transf.), A000421 (no loops), A085549, A129430, A129432, A129434, A129436.

Sequence in context: A101900 A005966 A082282 * A104859 A108289 A007779

Adjacent sequences:  A005964 A005965 A005966 * A005968 A005969 A005970

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Checked by Brendan McKay, Apr 15 2007

Using sequence A129427, terms a(12)-a(16) were computed in GAP by Ignat Soroko, Apr 07 2010

a(17)-a(19) added by Andrew Howroyd, Mar 19 2020

STATUS

approved

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Last modified July 8 02:24 EDT 2020. Contains 335503 sequences. (Running on oeis4.)