Solve the recurrence an 4 an 3 2an 2 4an 1 24an 0So

Solve the recurrence an + 4 + an + 3 - 2an + 2 + 4an + 1 - 24an = 0.

Solution

Let us consider a_(n+4) +a_(n+3) -2a_(n+3) +4a_(n+1) - 24a_n as a^4+a^3-2a^2+4a-24

= (a-2) (a+3) (a^2+4)

= a^4 + a^3 - 2 a^2 + 4 a - 24

=(-2 + a) (3 + a) (a^2 + 4)

Then the real roots are a = -3 or 2