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Linear Recurrence relations

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

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

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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-->

an= (A1 +A2x)(2)n + (B1 +B2x) (-2)n 

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