Find the solution to the following linear, homogeneous recurrence with constant coefficients:
an=8an−1−20an−2 for n≥2an=8an−1−20an−2 for n≥2 with initial conditions a0=0,a1=−12a0=0,a1=−12. The solution is of the form:

an=(α+iβ)(r+is)n+(α−iβ)(r−is)nan=(α +iβ)(r+is)n+(α−iβ)(r−is)n

For suitable real constants α,β,r, sα,β,r, s.

Find these constants and enter their values:

α =

β =

r =

s =

sα =