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Let n > 1 be an integer. Find all sequences a_1, a_2, \ldots a_{n^2 + n} satisfying the following conditions:
\text{ (a) } a_i \in \left\{0,1\right\} for all 1 \leq i \leq n^2 + n;
\text{ (b) } a_{i + 1} + a_{i + 2} + \ldots + a_{i + n} < a_{i + n + 1} + a_{i + n + 2} + \ldots + a_{i + 2n} for all 0 \leq i \leq n^2 - n
Author: unknown author, Serbia

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