
reccurence relations
In my notes I have the expression:
$\displaystyle a_n = 3a_{n1} + 2a_{n2}$
with
$\displaystyle a_0 = 1, a_1 = 2$
but I can't see how we get $\displaystyle a_0 = 1$
When I try I get
$\displaystyle 3a_{01} + 2a_{02}
= 3*1 + 2*2
= 3 + 4
= 7
$
so why is
$\displaystyle + 2a_{n2}
= 4$
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 $\displaystyle f(1)$ 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(21) + 2a(22)
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(31) + 2a(32)
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(41) + 2a(42)
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