title: Counting isomeric n-carbon aliphatic alkanes
body: <p>An n-carbon aliphatic alkane is an unrooted tree consisting of n nodes where the degree of each node is atmost 4. As an example, <a href="https://en.wikipedia.org/wiki/List_of_straight-chain_alkanes" rel="nofollow noreferrer">see this</a> for a list of the enumeration of some low values of n.</p>
  
  <p>I am looking for an algorithm to compute the number of such n-carbon aliphatic alkanes, given an n.</p>
  
  <p>I have <a href="https://chemistry.stackexchange.com/questions/16135/how-to-determine-number-of-structural-isomers">seen this</a> in chemistry stackexchange already. I have also thought of dynamic programming, i.e, building larger graphs from smaller components, but I cannot deal with overcounting the same isomers.</p>
  
  <p>Clarification: The Carbons are just a metaphor. I do not wish to take into account the instability of C16 and C17, nor do I care about stereoisomers</p>