Hello, Kev!

This one requires another trick . . .

The recurrence relation: . .[1]

Given: .

Consider the case: . .[2]

. . . . . . Multiply [1] by 4: . . .[3]

Subtract [3] from [2]: .

. . . . .

Let

Divide by

. . which factors; .

. . and has roots: .

. . . . . .Go for it!