Figure-It-Out Function! - Part 1: For 4 years

Algebra Level 5

A function \(f:\mathbb{Z}\rightarrow\mathbb{Z}\), has the following conditions

  • \(f(n)=\frac{f(n-1)+2f(\frac{n}{2})}{2}\), if \(n\) is even

  • \(f(n)=\frac{f(n)+2f(\frac{n-1}{2})}{2}\), if \(n\) is odd

If \(f(1)=2\), find \(\frac{f(2011)f(2012)f(2013)f(2014)}{f(3)f(4)f(10)f(12)f(18)f(52)f(60)f(502)}\)

This problem is part of the Figure-It-Out Function! series

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