Saturated acyclic alkanes show steric strain if they are highly branched and, in extreme cases, fall apart rapidly at room temperature. Consequently, attempts to count the number of isomeric forms for a given molecular formula that neglect this physical consideration will inevitably overestimate the size of the available chemical space. Here we derive iterative equations to enumerate the number of isomers (both structural and optical are considered separately) for the alkane series that take into account the inherent instability of certain carbon skeletons. These function by filtering out certain substructures from the graph representation of the molecule which have been found to be thermodynamically unstable. We use these relations to report new estimates of the size of physically accessible chemical space for acyclic alkanes and show that for large molecules there are more isomers that are structurally disallowed than there are allowed.