the characteristic of the form will be :
x^n = 18 x^n-1 - 65 x^ n-2
divide all term by x^n-2
x^2 = 18x - 65
x = 5 or x = 13
let f(n)= A(5)^n + B(13)^n
f(0)=0 ==> 0=A+B
f(1)=1 ==> 5A+13B=1
A= (-1/8) , B=(1/8)

f(n)=(1/8)*(13)^n - (1/8)*(5)^n
So f(1000)= (1/8)*(13)^1000 - (1/8)*(5)^1000

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