Find solution to a recurrence relation...

**vexiked** · March 20th 2009, 08:52 AM

I am stuck on this question, and do not know where to head with it.

Find the solution to An= 2An-1 + An-2 - 2An-3 for n=2,3,4,5......, with a0=3, a1=6 and a2=0

(Note that n-1, n-2, n-3 are subscripts)

**running-gag** · March 20th 2009, 09:32 AM

Hi

Well it depends by your level in maths
The characteristic polynomial is $x^3-2x^2-x+2$ whose roots are -1, 1 and 2

$a_n = \alpha \<img src=$ -1)^n + \beta \: 1^n + \gamma \: 2^n" alt="a_n = \alpha \

-1)^n + \beta \: 1^n + \gamma \: 2^n" />

$\alpha$ , $\beta$ , $\gamma$ values are found by the values of $a_0$ , $a_1$ , $a_2$

$a_n = -2 \<img src=$ -1)^n + 6 \:\: 1^n - 2^n" alt="a_n = -2 \

-1)^n + 6 \:\: 1^n - 2^n" />