A289991 Number of unlabeled connected simple graphs with n nodes of degree 4 or less and with at least a cyclic structure and a node of degree one.

0, 0, 0, 1, 7, 35, 181, 1027, 6551, 47356, 383353, 3439508, 33796286, 360254030, 4132780425, 50700507116, 661702767423, 9148018231984, 133481943863634, 2049205561735698, 33008193951255524, 556509843849858317, 9799223447550907197, 179855583136712491494

Offset: 1

Author

Natan Arie Consigli, Aug 03 2017

Keywords

• nonn

Comments

Number of alkyl-n-cycloalkanes with n carbon atoms (the pure n-cycloalkanes aren't counted here).

Stereoisomerism is not taken into account. Some of the drawn structures may or may not exist due to their strained geometries.

Examples

			a(5) = 7 because there are 7 structures with 5 carbons following the rule above: 1,1-dimethylcyclopropane, 1,2-dimethylcyclopropane, ethylcyclopropane, methylcyclobutane, 1-methylbicyclobutane, 2-methylbicyclobutane, methyltetrahedrane.
		

Crossrefs

Cf. A006820, A121941, A289159, A289989, A289990.

Formula

a(n) = A289159(n) - A289990(n).

a(n) = A121941(n) - A006820(n) - A289989(n). - Andrew Howroyd, Mar 20 2020

Extensions

a(0) removed and a(15)-a(24) from Andrew Howroyd, Mar 20 2020