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.

(In reply to computer solution and a fitted polynomial by Charlie)

The function is of course the sum of all the integers from zero to one less than n. 

Posted by Charlie on 2020-09-03 18:49:18