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

1,5

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.

Links

Table of n, a(n) for n=1..24.

Formula

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

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

Example

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.

Sequence in context: A037689 A051926 A297602 * A295248 A295647 A026128

Adjacent sequences: A289988 A289989 A289990 * A289992 A289993 A289994

Keyword

nonn

Author

Natan Arie Consigli, Aug 03 2017

Extensions

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

Status

approved