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

0,4

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

Links

Table of n, a(n) for n=0..24.

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.

Example

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.

Prog

(nauty/bash) geng -c -D4 ${n} -q | multig -m1 -D4 -u

Crossrefs

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

Sequence in context: A150193 A052300 A306832 * A150194 A150195 A363810

Adjacent sequences: A121938 A121939 A121940 * A121942 A121943 A121944

Keyword

nonn,nice

Author

Parthasarathy Nambi, Sep 03 2006

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

Status

approved