# Math Help - Reccurence relation

1. ## Reccurence relation

What is the form of the particular
solution of the linear non-homogeneous
recurrence relation
an= 8[an–2]– 16[an–4] + F(n)

F(n)=2

*** thE stuff IN THE [] SQUARE BRACKETS SHOULD BE SUB SCRIPTED]

The characteristic equation factorised is (x+ 2)^2(2x– 2)^2

2. ## Re: Reccurence relation

$x^4-8x^2+16 = (x+2)^2(x-2)^2$ (I'm not sure where you got the 2 before the second x).

Anyway, this equation has roots $\pm 2$, each with multiplicity 2. So, your general function is $a_n = c_1(-2)^n+c_2n(-2)^n+c_3\cdot 2^n+c_4 n\cdot 2^n + k(n)$ where $k(n)$ is the solution to the non-homogeneous portion of the relation. According to WolframAlpha, $k(n) = \dfrac{2}{9}$.