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A peculiar function! (Posted on 2020-09-03) |
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f(n)=max{f(j)+f(n−j)+j}
Let f be a function from the set of positive integers to the set of non-negative integers such that f(1)=0 and f(n) is defined as of above for n≥2. Determine the value of f(2020).
Note: The maximum in the definition of f(n) is considered over all j such that 1≤j≤n−1, i.e for all j for which f(n) and f(n−j) are defined.
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