1, 3, 1+3, 13, what's next?

Level pending

Let a and b be two constants such that ax + by = 1, a\(x^2\)+ b\(y^2\) =3, a\(x^3\) + b\(y^3\) = 4, a\(x^4\) + b\(y^4\) = 13 and a\(x^5\) + b\(y^5\) = m/n where m and n are coprime positive integers. What is m+n?

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