What you need to do is to employ 3 555 ICs:
- The first (astabile) will be generating square wave of 20ms/220ms;
- The second (monostabile) will be trigged by the first one anw will generate single pulse of 120ms;
- The third (monostabile) will be trigged by the second one and will generate single pulse of 20ms ..
On how to connect 555s in stages see picture below .. for your project you will need to loop the output of the first 555 to itself to configure it as astabile ( **broken link removed** ), and remove the loop betwenn IC3 and IC1 ..
So, in your case you will be using otputs A and C ..
Regards,
IanP