A Sequence $d _ { 1 } , d _ { 2 } , d _ { 3 } , \ldots$

question 9

Essay

A sequence $d _ { 1 } , d _ { 2 } , d _ { 3 } , \ldots$ satisfies the recurrence relation $d _ { k } = 8 d _ { k - 1 } - 16 d _ { k - 2 }$ with initial conditions $d _ { 1 } = 0$ and $d _ { 2 } = 1$ . Find an explicit formula for the sequence.