cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A289990 Number of unlabeled connected simple graphs with n nodes of degree 4 or less and degree at least 2 which are not 4-regular graphs.

Original entry on oeis.org

0, 0, 1, 3, 10, 37, 161, 878, 5605, 41912, 355558, 3359250, 34723752, 388248880, 4655392910, 59493136018, 806368182523, 11546555440892, 174096392201350, 2756178999408121, 45700016438834847, 791855740761714317, 14309459324411915139, 269188219981362999139
Offset: 1

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Author

Natan Arie Consigli, Aug 03 2017

Keywords

Comments

This is the number of pure n-cycloalkylic structures with n carbon atoms.
Stereoisomerism is not taken into account. Some of the drawn structures may or may not exist due to their strained geometries.

Examples

			a(4) = 3, because here are 3 molecules with 4 carbons following the above rule: cyclobutane, bicyclobutane, tetrahedrane.
a(5) = 10, because there are 10 molecules with 5 carbons following above rule: cyclopentane, housane, spiropentane, pyramidane, bicyclopentane, propellane, tricyclo[2.1.0.0^(1,3)]pentane, tricyclo[2.1.0.0^(2,5)]pentane, tetracyclopentane, pentacyclopentane.

Crossrefs

Cf. A006820, A121941, A289989, A289991.

Formula

a(n) = A289989(n) - A006820(n).

Extensions

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

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.

Original entry on oeis.org

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

Views

Author

Natan Arie Consigli, Aug 03 2017

Keywords

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
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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