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%I M5345 #32 Feb 17 2024 05:32:50
%S 1,0,1,70,19320,11166120,11543439600,19491385914000,50233275604512000,
%T 187663723374359232000,975937986889287117696000,
%U 6838461558851342749449120000,62856853767402275979616458240000,741099150663748252073618880960000000,10997077750618335243742188527076864000000
%N Number of connected trivalent (or cubic) labeled graphs with 2n nodes.
%D R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958.
%D R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
%D R. W. Robinson, Computer print-out, no date. Gives first 29 terms.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A004109/b004109.txt">Table of n, a(n) for n = 0..100</a> (terms 1..29 from R. W. Robinson)
%H R. C. Read, <a href="/A002831/a002831.pdf">Letter to N. J. A. Sloane, Feb 04 1971</a> (gives initial terms of this sequence)
%H R. W. Robinson, <a href="/A002829/a002829.pdf">Cubic labeled graphs, computer print-out, n.d.</a>
%F Conjecture: a(n) ~ 2^(n + 1/2) * 3^n * n^(3*n) / exp(3*n+2). - _Vaclav Kotesovec_, Feb 17 2024
%e From _R. J. Mathar_, Oct 18 2018: (Start)
%e For n=3, 2*n=6, the A002851(n)=2 graphs have multiplicities of 10 and 60 (sum 70).
%e 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)
%Y See A002829 for not-necessarily-connected graphs, A002851 for connected unlabeled cases.
%Y Cf. A324163.
%K nonn,nice
%O 0,4
%A _N. J. A. Sloane_
%E a(0)=1 prepended by _Andrew Howroyd_, Sep 02 2019
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