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URL: https://oeis.org/A004109

⇱ A004109 - OEIS

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A004109
Number of connected trivalent (or cubic) labeled graphs with 2n nodes.
8
1, 0, 1, 70, 19320, 11166120, 11543439600, 19491385914000, 50233275604512000, 187663723374359232000, 975937986889287117696000, 6838461558851342749449120000, 62856853767402275979616458240000, 741099150663748252073618880960000000, 10997077750618335243742188527076864000000
OFFSET
0,4
REFERENCES
R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
R. W. Robinson, Computer print-out, no date. Gives first 29 terms.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..100 (terms 1..29 from R. W. Robinson)
Élie de Panafieu, Asymptotic expansion of regular and connected regular graphs, arXiv:2408.12459 [math.CO], 2024. See p. 13.
R. C. Read, Letter to N. J. A. Sloane, Feb 04 1971 (gives initial terms of this sequence)
FORMULA
Conjecture: a(n) ~ 2^(n + 1/2) * 3^n * n^(3*n) / exp(3*n+2). - Vaclav Kotesovec, Feb 17 2024
EXAMPLE
From R. J. Mathar, Oct 18 2018: (Start)
For n=3, 2*n=6, the A002851(n)=2 graphs have multiplicities of 10 and 60 (sum 70).
For n=4, 2*n=8, the A002851(n)=5 graphs have multiplicities of 3360, 840, 2520, 10080 and 2520, (sum 19320). (The orders of the five Aut-groups are 8!/3360 =12, 8!/840=48, 8!/2520 =16, 8!/10080=4 and 8!/2520=16, i.e., all larger than 1 as indicated in A204328). (End)
CROSSREFS
See A002829 for not-necessarily-connected graphs, A002851 for connected unlabeled cases.
Cf. A324163.
Sequence in context: A103157 A364305 A007099 * A002829 A177637 A145410
KEYWORD
nonn,nice
EXTENSIONS
a(0)=1 prepended by Andrew Howroyd, Sep 02 2019
STATUS
approved