$$f(1)=3 \quad f(2)=6\quad f(3)=18\quad f(4)=36 \quad f(5)=108$$

How can I define this function? The function is recursive and multiplies by 2 then 3 alternatively. I know I could solve this in code, but I'm not sure of the mathematical terms one could use to make a function like this.
Let me know if I'm not clear and thank you for any help.