Here a challenge for all the GoIIT members,Experts and Administrators!!I am sick and tired

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To summarize:

Let $k = \left[ \frac{n}{2} \right]$

Suppose n is even, then $f(n) = k + \left[ \frac{k+1}{2} \right]+1$

Suppose n is odd, and of the form 4s+1, then $f(n) = k + \left[ \frac{k}{2}\right]+2$

Suppose n is odd, and of the form 4s-1, then $f(n) = k + \left[ \frac{k+1}{2}\right]+2$

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