Express the solution of the linear nonhomogenous recurrence relation $a_{n} = a_{n-1} + a_{n-2} + 1\:\text{for}\: n \geq 2
\:\text{where}\: a_{0} = 0\:\text{and}\: a_{1} = 1$ in terms of the Fibonacci numbers. [Hint: Let $b_{n} = a_{n + 1}$ and apply question $42$ to the sequence $b_{n}.]$
