Hurwitz's counting isomers of alkanes (Q294084)

From the text: Adolf Hurwitz's last diary contains an entry of ten pages length related to the counting problem of isomers of alkanes, bearing the date 20 May 1918. The short introduction to the problem shows that Hurwitz knew about Cayley's work, for counting the isomers of hydrocarbons \(\mathrm{C}_n \mathrm{H}_{2n+2}\), however, Hurwitz followed another strategy. In this article, this strategy is explained in detail.