A283416 Number of possible connected steric graphs with n nodes of degree less than 5.

1, 1, 2, 8, 43, 405

Offset

1,3

Comments

This gives the number of hypothetical neutrally charged saturated carbon allotropes and hydrocarbons (alkanes, cycloalkanes, alkyl-cycloalkanes) with n carbon atoms satisfying the octet rule counting all isomers, except conformers.

Steric (three-dimensional) graphs can be represented as two-dimensional graphs provided that stereoisomers are taken into account. This means acting the group S_4 on the stereocenters (nodes with 4 different substituents) of each 2D graph and counting all of the resulting non-symmetric molecules.

Many of those "theoretical" molecules are to be discovered and some may not exist due to their strained geometries.

The terms of this sequence (and related ones) were found by drawing and counting the molecules in the PDFs below. If there are any missing molecules you can contact me. I'll add them in the PDF and update the data section.

Links

Table of n, a(n) for n=1..6.

Natan Arie' Consigli, Illustration of a(5) and a(6)

Example

a(4) = 8 because there are eight structures with 4 nodes (carbons) following the above rules: butane, isobutane, cyclobutane, methylcyclopropane, (r,r)-bicyclobutane, (s,s)-bicyclobutane, (r,r,r)-tetrahedrane, (s,s,s)-tetrahedrane.

Crossrefs

Row sums of A280013.

Sequence in context: A276497 A324670 A334335 * A075817 A374673 A264565

Adjacent sequences: A283413 A283414 A283415 * A283417 A283418 A283419

Keyword

nonn,more,hard

Author

Natan Arie Consigli, Mar 07 2017

Status

approved