Three identical integers greater than 1 are written on a board. One of the numbers is rubbed off and replaced by a number which is one less than the sum of the other tow. This process is repeated a number of times.

Gerry wants to get the number 2010 from as many starting triples a,a,a as possible. One way of couse is to start with 2010, 2010,2010. What are all the other ways?

Thank you for you help!!