A121941 Number of unlabeled connected simple graphs with n nodes of degree 4 or less.

1, 1, 1, 2, 6, 21, 78, 353, 1929, 12207, 89402, 739335, 6800637, 68531618, 748592936, 8788983173, 110201690911, 1468157196474, 20695559603921, 307590282700915, 4805537369573319, 78710267083015571, 1348394635886684901, 24109112440149231355, 449050443283294835914

Offset: 0

Author

Parthasarathy Nambi, Sep 03 2006

Keywords

• nonn
• nice

Comments

Number of graphs of hydrogen bonded water clusters.

This counts the connected graphs where each vertex has degree 4 or less. - Charles R Greathouse IV, Jul 07 2017

Also number of saturated hydrocarbons and allotropes with n carbon, or valence 4, atoms (excluding stereoisomers) following the octet rule. - Natan Arie Consigli, Jul 07 2017

Examples

			With 4 carbons, n-butane, i-butane, cyclobutane, bicyclobutane, methylcyclopropane and tetrahedrane are the 6 isomers satisfying the property above, so a(4)=6. - _Natan Arie Consigli_, Jul 07 2017
If n=5 then the number of graphs of hydrogen bonded water clusters is 21.
		

Links

• G. Brinkmann, Generating water clusters and other directed graphs, J. Math. Chem. 46 (4) (2009) 1112-1121, Table 1.
• T. Miyake and M. Aida, Enumeration of topology-distinct structures of hydrogen bonded water clusters, Chem. Phys. Lett., vol. 363 (2002) pp. 106-110. See Table 1 column 2 on page 109.

Crossrefs

Cf. A121942, A243393 (degree 3 or less), A287424 (excludes allotropes), A289157, A289158, A303032 (degree 5 or less).

Programs

nauty

geng -c -D4 ${n} -q | multig -m1 -D4 -u

Extensions

More terms sent by Natan Arie Consigli, Jul 07 2017

Renamed by Andrew Howroyd, Mar 19 2020 based on comment by Charles R Greathouse IV.

a(16)-a(24) from Andrew Howroyd, Mar 19 2020