Henze H.R., Blair Ch.M. The number of isomeric hydrocarbons of the methane series

Journal of the American Chemical Society, 1931, Vol. 53, No 8, pp. 3077–3085.At various times attempts have been made by both mathematicians and chemists to derive a formula by which the number of isomeric hydrocarbons of the methane series could be calculated. Attempts to derive such a formula soon showed that no direct or simple relationship appears to exist between the total number of isomeric hydrocarbons of the methane series and their carbon content.By means of a separation of the isomeric hydrocarbons of each specified carbon content into types, arbitrarily chosen upon the basis of their structural formulas, a relationship may be established between the number of hydrocarbons and the alkyl groups of which the former may be considered to be composed. Mathematical formulas of the (finite) recursion type are advanced which permit of the calculation, from their carbon content, of the number of isomeric hydrocarbons in each of these structural types. In using these recursion formulas to calculate the total number of such hydrocarbons of any given carbon content, the total number of alkyl groups (i.e., the total number of isomeric alcohols) of N/2 and all lesser carbon contents must be known.The totals obtained by use of these mathematical formulas agree exactly through the tetradecanes with the numbers required by theory as tested by actually writing all the possible structural formulas.