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base 2 numerical system

Source: II Soros Olympiad 1995-96 R3 11.9 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 6, 2024
number theory

Problem Statement

Let us denote by b(n)b(n) the number of ways to represent nn in the form n=a0+a1⋅2+a2⋅22+...+ak⋅2k,n = a_0+a_1 \cdot 2 +a_2 \cdot 2^2+...+ a_k \cdot 2^k, where the coefficients at, r=1r = 1,22,......, kk can be equal to 00, 11 or 22. Find b(1996)b(1996).
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