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crazy recurrence relation

Name: Anonymous 2009-12-10 0:57

I know how to get the closed form of linear homogeneous recurrence relations such as
a_0 = 1, a_1 = 1

a_n = a_{n-1} + a_{n-2}


But I have no idea how to do this:
a_0 = 1, a_1 = 10,

a_n = \frac{a_n - 1}{a^5_{n-2}}, n >= 2

Can I get a clue on how to solve this one? Maybe a link to a similar relation getting solved?

Name: Anonymous 2009-12-10 12:17

Alright, I've gotten to the general solution of b_{n} as shown here: http://i46.tinypic.com/4t5xe8.png
I'm not supposed to use i in my answer, but I can't figure out how to do that since there is no x that satisfies (1 + sqrt(19)) / 2 = sin(x) + cos(x).
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