please help..

if f(n+1) = max{ f(k) + f(n-k+1) + 1} for 1 <= k <= n; f(1)  = 0.
Find f(n+1) in terms of n.
Eg: f(4) = ? n = 3; 1<= k <= 3; f(4) = max{f(1) + f(3) + 1, f(2) +
f(2)+1, f(3) + f(1) +1}

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