Linear Recurrence relations

Question

$\text{What is the general form of homogeneous solution for linear nonhomogeneous recurrence relation }$

$a_n = 8 a_{n-2} - 16a_{n-4}$

Answer 1

let aⁿ= t⁴ than aⁿ-2= t2 and aⁿ-4=1

solving the given equation as-- > characteristics equation -- > 

t⁴=8t²-16

t⁴-8t²+16=0

(t²-4)²=0

(t-2)² (t+2)² =0

t= +2 and t= -2

since the roots are real and unequal and in the second order-->

a_n= (A₁ +A₂x)(2)ⁿ + (B₁ +B₂x) (-2)ⁿ 

Answer

Comments

Can you please provide the theory part for solving this question?