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no of sequences with terms in {0,1,2,3} so that n=a_0+2a_1+2^2a_2+...+2^na_n

Source: Polish National Olympiad 2015 2nd round, p5

August 28, 2019
algebranumber theorycombinatorics

Problem Statement

Let nn be a positive integer. Determine the number of sequences a0,a1,…,ana_0, a_1, \ldots, a_n with terms in the set {0,1,2,3}\{0,1,2,3\} such that n=a0+2a1+22a2+…+2nan.n=a_0+2a_1+2^2a_2+\ldots+2^na_n.
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