A289158 Number of unlabeled connected loopless multigraphs with n nodes of degree 4 or less and with at most double edges.

1, 1, 2, 7, 28, 112, 590, 3419, 23453, 178599, 1516692, 14083855, 142029043, 1542152723, 17925912574, 221938298129, 2914638247016, 40455853460661, 591654481313077, 9091698010380468, 146433114305147508, 2466517505722469501, 43361349681960337334

Offset

0,3

Comments

In chemical terms this counts the following molecules (excluding stereoisomers) without triple bonds, given n carbon atoms:

- carbon allotropes;

- aliphatic hydrocarbons;

- resonance structures of graphically non-equivalent anti-aromatic and aromatic hydrocarbons;

Some molecules are theoretical and may or may not exist.

Links

Table of n, a(n) for n=0..22.

Daniel R. Herber, Enhancements to the perfect matching approach for graph enumeration-based engineering challenges, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2020).

Prog

(nauty/bash) geng -c -D4 ${n} -q | multig -m2 -D4 -u

Crossrefs

Cf. A121941, A289157 (allows more than two edges), A303030, A303031.

Sequence in context: A289607 A068944 A215143 * A012855 A224066 A150646

Adjacent sequences: A289155 A289156 A289157 * A289159 A289160 A289161

Keyword

nonn

Author

Natan Arie Consigli, Jul 04 2017

Extensions

a(15)-a(22) from Andrew Howroyd, Mar 20 2020

Status

approved