Tree numbers

[Gary Rosenberg]

The progession is the product of the odd numbers. 

Taxa  Trees

2        1
3        3
4        15
5        105
6        945
7        10395

The formula is (2n-3)! / ((2 to the power (n-2)) x (n-2)!), where n = number of taxa.

Also, the number of monophyletic groups in a given dichotomous tree of n taxa is 2n-1 and the number of orthophyletic groups is (n-1)(n-2).

Gary

""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
Gary Rosenberg, Ph.D.                  rosenberg at ansp.org
Academy of Natural Sciences            http://www.acnatsci.org
1900 Benjamin Franklin Parkway         Phone 215-299-1033
Philadelphia, PA 19103-1195 USA        Fax   215-299-1170