Calculating future occurrences of Friday the 13th

Question

I\'d like to be able to start with a year, and calculate occurrences of Friday the 13th. A brute force solution is easy and obvious. I have something slightly better, but

Answer 1

One thing I noticed is that the first of the month falls on a Sunday during months with a Friday the 13th. You can probably leverage this to make it easier to calculate.