Hey,

I was trying to solve this expected value problem. I was thinking of using indicator random variables and linearity of expectation but somehow couldn't arrive at the answer. Please help.

Problem: Given a number N, take any random permutation of numbers R = [1, 2, ..., N]. You need to find the expected number of special points in the resulting permutation. An element R[i] is special if:
1. R[i] = R[i-1] + R[i+1] (for 1 <=i <= N-2)
2. R[i] = 2*R[i+1] (for i==0)
3. R[i] = 2*R[i-1] (for i==N-1)

Return the denominator and numerator of the answer. (Fraction should not be further reducible)