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

1, 1, 2, 4, 12, 22, 68, 166, 534, 1589, 5464, 18579, 68320, 255424, 1000852, 4018156, 16671976, 70890940, 309439942, 1381815168, 6310880471, 29428287639, 140012980007, 678970863717, 3353545264060, 16857749613964, 86191265140699, 447951112379963, 2365177154077186

Offset: 0

Author

Natan Arie Consigli, Apr 17 2018

Keywords

• nonn

Comments

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.

Some of the molecules are theoretical and may or may not exist due to their strained geometries.

Apparently the same as A243391 for n > 2. - Georg Fischer, Oct 16 2018

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

Examples

			a(3) = 4 because there are 4 molecules satisfying the above condition: triazane, triazene, triazirine, triazidirine.
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).
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
		

Crossrefs

Cf. A134818, A243391, A289158, A303031.

Programs

nauty

for n in {1..18}; do geng -c -D3 ${n}  -q | multig -m2 -D3 -u;done

Formula

a(n) = A243391(n) for n > 2. - Andrew Howroyd, Mar 20 2020

Extensions

a(20)-a(28) from Andrew Howroyd, Mar 20 2020