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How many ways are there of writing $n$ as a sum of odd integers, where the order doesn't matter? For example, there are $2$ ways of writing $3$: $(1,1,1)$ and $(3)$.

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A difficult problem, for which there are no nice formulas. A famous theorem of Euler shows that the number is the same as the number of partitions of $n$ into distinct parts. Doesn't really help much. –  André Nicolas May 27 at 16:12
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OEIS A000009 –  Henry May 27 at 16:16

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