10 day cycle where I work in the UK, with 6 duty days and 4 rest days. Over the year, that's 36.5 cycles, with total of 219 duty days. No leave factored in, so you can knock 30+ days off that duty day total depending on your leave allowance.
Number of weekends off duty are not a factor in any employee agreement. We get paid an unsocial hours payment and therefore are liable for duty on weekends, public holidays, nights, etc, etc. It is dependent on where the rest days on your cycle fall whether you get a weekend off or not.