A280006 Number of possible connected steric graphs with n nodes of degree less than 5, excluding the ones with all nodes of degree 4 and trees.

0, 0, 1, 6, 39, 399

Offset: 1

Author

Natan Arie Consigli, Jan 02 2017

Keywords

• nonn
• more
• hard

Comments

Also number of hypothetical neutrally charged hydrocarbons with n carbon atoms containing a cyclic set of atoms (cycloalkanes and alkyl-cycloalkanes) satisfying the octet rule. This includes 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.

The terms of this sequence (and related ones) were found by drawing and counting the hydrocarbons 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.

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

Links

• Natan Arie' Consigli, Illustration of a(5) = 39: molecules with 5 carbons
• Natan Arie' Consigli, Illustration of a(6) = 399: molecules with 6 carbons

Crossrefs

Cf. A000628 (counts acyclic alkanes), A000639 (counts alkyl-benzenes).

Formula

a(n) = A280012(n) - A000628(n).