Exercise A

Posted 02/21/2015
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A partition of a natural number `n` is a way of writing `n` as a sum of positive integers.

For example `\alpha=(4,2,2,2,1,1)=(4,2^3,1^2)` is a partition of `12` and has `4,2,1` as parts. The number of parts of `\alpha` is `6`.

`a(n)` is the number of all the partitions of `n`.
For example, `a(3)=3` because `3=2+1=1+1+1` and `a(4)=5` because `4=3+1=2+2=2+1+1=1+1+1+1`.

Find `a(n)`.