cp's OEIS Frontend

A303030 Number of unlabeled connected loopless multigraphs with n nodes of degree 3 or less and with single or double edges.

%I A303030 #36 Jun 02 2025 17:24:36
%S A303030 1,1,2,4,12,22,68,166,534,1589,5464,18579,68320,255424,1000852,
%T A303030 4018156,16671976,70890940,309439942,1381815168,6310880471,
%U A303030 29428287639,140012980007,678970863717,3353545264060,16857749613964,86191265140699,447951112379963,2365177154077186
%N A303030 Number of unlabeled connected loopless multigraphs with n nodes of degree 3 or less and with single or double edges.
%C A303030 For n >= 1, a(n) is also the number of hydronitrogen molecules containing only n nitrogen trivalent (octet rule satisfying) atoms. So for example, diazene is counted but hydrazoic acid is not because the former has only trivalent nitrogens and the latter has two non-trivalent nitrogens.
%C A303030 Some of the molecules are theoretical and may or may not exist due to their strained geometries.
%C A303030 Apparently the same as A243391 for n > 2. - _Georg Fischer_, Oct 16 2018
%C A303030 This is the case since A243391 gives the number of loopless multigraphs with nodes of degree 3 or less. The extra graph in A243391 is the 3-regular graph on 2 nodes. - _Andrew Howroyd_, Mar 20 2020
%F A303030 a(n) = A243391(n) for n > 2. - _Andrew Howroyd_, Mar 20 2020
%e A303030 a(3) = 4 because there are 4 molecules satisfying the above condition: triazane, triazene, triazirine, triazidirine.
%e A303030 Note: hydrazoic acid is not counted because there are 2 nitrogens not satisfying the octet rule (one has a positive formal charge and the other one has a negative one).
%e A303030 Graphically, a(3) = 4 because there are 4 graphs satisfying the above condition: the linear graph, the linear graph with one double edge, the triangle graph, and the triangle graph with one double edge. - _Michael B. Porter_, Apr 28 2018
%o A303030 (nauty) for n in {1..18}; do geng -c -D3 ${n}  -q | multig -m2 -D3 -u;done
%Y A303030 Cf. A134818, A243391, A289158, A303031.
%K A303030 nonn
%O A303030 0,3
%A A303030 _Natan Arie Consigli_, Apr 17 2018
%E A303030 a(20)-a(28) from _Andrew Howroyd_, Mar 20 2020