Put n=0 in f(n+1)=f(n)+3f(n-1) and we get: f(1)=f(0)+3f(-1). But we know f(0)=-1 and f(1)=2, so plug these into the equation: 2=-1+3f(-1), so f(-1)=3/3=1. Now we have f(-1)=1, f(0)=-1 and f(1)=2. We can find f(2)=f(1)+3f(0)=2-3=-1. we find f(3) by putting in n=2: f(3)=f(2)+3f(1)=-1+6=5; f(4)=f(3)+3f(2)=5-3=2. This is building into a pattern: 1, -1, 2, -1, 5, 2,... The series of f values involves the previous two values or terms: add the last term to 3 times the one before to get the next f value. So to continue beyond f(4), we take 2 and add on 3*5=17; then we take 17 and add on 3*2=23, and so on: 1, -1, 2, -1, 5, 2, 17, 23, 74...