Can you please help me to obtain the generating function of the recurrence relation
ar =ar-l + ar-z with ao = 0, al = 2, az = 3.
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?
I assume this is a Fibonacci-type sequence . . .Can you please help me to obtain the generating function of the recurrence relation
ar =ar-l + ar-z with ao = 0, al = 2, az = 3. . . . this is wrong!
$\displaystyle a_n \:=\:a_{n-1} + a_{n-2}\quad\text{ with }a_0 = 0,\;a_1= 2 \quad \hdots\text{ and }a_2\text{ is }not\text{ equal to 3 !}$
. . 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 . . .