Follow bottom-up approach in such questions. like first calculate f(0) then f(1) and so on , because there are recursive calls and functions are evaluated in post order so better start from leaf ..
f(0)=1 //obvious
f(1)=1 // obvious
f(2)= ? i=2 i=1
r=0+f(2/3)=0+f(0)=1 r=1+f(1/3)=1+f(0)=1+1=2
f(2)=2
f(3)=? i=3 i=2 i=1
r=0+f(3/3)=0+f(1)=0+1=1 r=1+f(2/3)=1+1=2 r=2+f(1/3)=2+1=3
f(3)=3
f(4)=?
i=4 i=3
r=0+f(4/3)=0+f(1)=1 r=1+f(3/3)=1+f(1)=2
i=2 i=1
r=2+f(2/3)=2+f(0)=3 r=3+f(1/3)=4
f(4)=4
f(5)=?
i=5 i=4 i=3
r=0+f(5/3)=0+f(1)=1 r=1+f(4/3)=2 r=2+f(3/3)=2+f(1)=3
i=2 i=1
r=3+f(2/3)=3+1=4 r=4+f(1/3)=4+f(0)=5
f(5)=5
f(6)=?
i=6 i=5 i=4
r=0+f(6/3)=0+f(2)=2 r=2+f(5/3)=3 r=3+f(4/3)=4
i=3 i=2 i=1
r=4+f(3/3)=5 r=5+f(2/3)=6 r=6+f(1/3)=6+f(0)=7
f(6)=7