A004109 Number of connected trivalent (or cubic) labeled graphs with 2n nodes.

1, 0, 1, 70, 19320, 11166120, 11543439600, 19491385914000, 50233275604512000, 187663723374359232000, 975937986889287117696000, 6838461558851342749449120000, 62856853767402275979616458240000, 741099150663748252073618880960000000, 10997077750618335243742188527076864000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Examples

			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)
		

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)
• R. W. Robinson, Cubic labeled graphs, computer print-out, n.d.

Crossrefs

See A002829 for not-necessarily-connected graphs, A002851 for connected unlabeled cases.

Cf. A324163.

Formula

Conjecture: a(n) ~ 2^(n + 1/2) * 3^n * n^(3*n) / exp(3*n+2). - Vaclav Kotesovec, Feb 17 2024

Extensions

a(0)=1 prepended by Andrew Howroyd, Sep 02 2019