Calculate the number of 4-tip caterpillars.
References
Chindelevitch, Leonid, et al. "Network science inspires novel tree shape statistics." PloS one 16.12 (2021): e0259877. Rosenberg, Noah A. "The mean and variance of the numbers of r-pronged nodes and r-caterpillars in Yule-generated genealogical trees." Annals of Combinatorics 10 (2006): 129-146.