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

1, 1, 2, 8, 43, 405

Offset: 1

Author

Natan Arie Consigli, Mar 07 2017

Keywords

• nonn
• more
• hard

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.

Examples

			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.
		

Links

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

Crossrefs

Row sums of A280013.