Problem #46
When Butter Recurses
Let us define a series M such that M(n-1) + M(n+1) = 5*F(n) where F(n) is the n^{th} term of the Fibonacci sequence with F(0) = 0, F(1) = 1 and M(0)=2.
Find the value of \prod_{n=1}^{9} M(2^n)
Give answer \mod 1000000007