Find coefficient of $x^{18}$ in $(1+x^3+x^6+x^9+\cdots)^6 $
Normally, to to this I would look for a pattern that follows the following basic expansions in this powerpoint: http://academics.smcvt.edu/jellis-monaghan/combo2/Archive/Combo%20s03/class%20notes%20s03/seection6_2.ppt
However, what's throwing me off is the doubling exponents. I'm not quite sure how exactly to deal with them. Any help would be appreciated.