In how many ways can 100 be written as a sum of (non-negative integer) powers of 3? For example, one way would be 100 = 27 + 27 + 9 + 9 + 9 + 9 + 9 + 1. Note that powers may be repeated and that order does not matter.

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Source: Japanese Mathematical Olympiad
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The solution will be posted shortly.
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