# Recursive Recursion - 1

**Discrete Mathematics**Level 5

\[ \large \begin{array} {l l }

a_{n} & = a_{n+1}a_{n-1} - b_{n+1}b_{n-1} \\
b_{n} & = b_{n+1}a_{n-1} + a_{n+1}b_{n-1} \\ \end{array} \]

Consider, two recursive relations defined as above with initial starting conditions \(a_{0} = 1\), \(b_{0} = 2 \), \(a_{1} = 3\) and \(b_{1} = 4\).

If the value of \(a_{2015}^{2} + b_{2015}^{2}\) can be expressed as \(\dfrac{x}{y}\), where \(x\), \(y\) are coprime integers. Find the value of \(x+y\).