Rooted catafusene

Figure 9 Bond-rooted catafusenes. (a) 5-catafusene. Only one hexagon adjoins the hexagon with the root bond (thick line), b) D-catafusene. Two hexagons adjoin the hexagon with the root bond.

The X on the right-hand side come from the fact that l/j = 1, whereas Si=Di = 0. Substituting Eq. [21] into Eq. [22] we derive the counting series for bond-rooted catafusene hydrocarbons ... 

Figure 10 The four types of rooted catafusenes. The root hexagon is the shaded one. (i) Only one hond-rooted catafusene is attached ) two bond-rooted catafusenes are attached in meta position (Hi) two bond-rooted catafusenes are attached in para position and (iv) three bond-rooted catafusenes are attached.

We now wish to count catafusenes in which one hexagon (the root) has been distinguished from the other. Such a rooted catafusene is obtained by taking the root hexagon and attaching one, two, or three of its bonds to a bond-rooted catafusene. As depicted in Figure 10, this process can be performed in four ways. 

Let S and D denote the numbers of S-catafusenes and D-catafusenes having n hexagons, and let + D be the total of bond-rooted catafu-... 

Zhang FJ, Guo XF, Cyvin SJ, Cyvin BN (1992) The Enumeration of Catafusenes Rooted at a Polygon Core. Chem Phys Letters 190 104... 

---