Thread: reccurence relations

In my notes I have the expression:


with


but I can't see how we get

When I try I get


so why is


to get -3 + 4 = 1

obviously I am not understanding something...
can you point out where I am going wrong please?
Thanks

Go to this web link. You can change values for click the equals sign. You will see how the recursion changes.

Now why? Well we need to know how the initial values because we have two definiting terms.

That's a great link, I'm sorry but I still don't get it.
if I'm looking for f(4)
then
f(2) = 3a(2-1) + 2a(2-2)
f(2) = 3*a(1) + 2*a(0) <---- where a(1) = 2 and a(0) = 1
f(2) = 3*2 + 2*1
f(2) = 8

f(3) = 3a(3-1) + 2a(3-2)
f(3) = 3*a(2) + 2*a(1) <----a(2) = 8, a(1) =2
f(3) = 3*8 + 2*2
f(3) = 28

f(4) = 3a(4-1) + 2a(4-2)
f(4) = 3*a(3) + 2*a(2) <-----a(3)=28, a(2) = 8
f(4) = 3*28 + 2*8
f(4) = 100

is that right?
(I think I was reading too deep into things when i was trying to figure out how a(0) = 1, I guess it's just a given because a(0) =1 and a(1) = 2 are initial values, we don't need to work out how to get them, we just use them to find higher values??)

Just wandering if I have worked through this correctly or not?
Thanks for your time