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

1,4

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

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

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

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

Formula

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

Crossrefs

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

Sequence in context: A006678 A252761 A145709 * A336291 A034661 A094654

Adjacent sequences: A280003 A280004 A280005 * A280007 A280008 A280009

Keyword

nonn,more,hard

Author

Natan Arie Consigli, Jan 02 2017

Status

approved