For each positive integer n, let f(n) denote the number of ways of representing n as a sum of powers of 2 with nonnegative integer exponents. Representations which differ only in the ordering of their summands are considered to be the same. For instance, f(4)=4, because the number 4 can be represented in the following four ways: 4,2+2,2+1+1,1+1+1+1. Prove that, for any integer n≥3, 2n2/4<f(2n)<2n2/2. inequalitiesAdditive Number Theory