Functions, Can you solve this?

Algebra Level 5

\[\large f(m+1) = (-1)^{m+1} m - 2f(m) \]

Let function \(f\), true for integers \(m\), satisfy the above equation and \(f(1) = f(2009)\). If \(\displaystyle \sum_{k=1}^{2008} f(k) = \Phi\), find \(3 \Phi\).

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