1. ## Recurrence relation

ar =ar-l + ar-z with ao = 0, al = 2, az = 3.

2. Originally Posted by bond

ar =ar-l + ar-z with ao = 0, al = 2, az = 3.
Is ar-1 meant to be $\displaystyle a_{r-1} ?$

What is ar-z meant to be? Do you mean $\displaystyle a_{r-2} ?$

Is az = 3 meant to be $\displaystyle a_2 = 3 ?$

Note: z is not the same as 2.

3. I think it looks like this

ar =ar-l + ar-z

with ao = 0, al = 2, az = 3

4. Originally Posted by bond
I think it looks like this

ar =ar-l + ar-z

with ao = 0, al = 2, az = 3
Writing the same thing bigger doesn't clarify anything.

5. ## Please see the attachment

Please see the attachment, I have typed in the question in the MS Word file.

Thanks.

6. Hello, bond!

Does it really help to write things in a different color and in
a smaller font?

And if you have no idea what's going on, why are you working on this problem?

ar =ar-l + ar-z with ao = 0, al = 2, az = 3.
. . . this is wrong!
I assume this is a Fibonacci-type sequence . . .

$\displaystyle a_n \:=\:a_{n-1} + a_{n-2}\quad\text{ with }a_0 = 0,\;a_1= 2 \quad \hdots\text{ and }a_2\text{ is }not\text{ equal to 3 !}$
. . Each term is the sum of the preceding two terms.

The sequence is: .$\displaystyle 0,2,2,4,6,10,16, 26, \hdots$

The terms are exactly twice that of the original Fibonacci sequence

. . whose formula is: .$\displaystyle F_n \:=\:\frac{(1+\sqrt{5})^n - (1-\sqrt{5})^n}{2^n\sqrt{5}}$

Therefore: .$\displaystyle a_n \;=\;2\cdot\frac{(1+\sqrt{5})^n - (1-\sqrt{5})^n}{2^n\sqrt{5}}$

Does that help?

I didn't think so . . .