Number of Distinct Partitions
Find the number of different ways to write N = 36 as the sum of positive integers.
Two sums that differ by the order of these positive integers is counted once.
As an example, if N were equal to 4 then it can written as
4
3 + 1
1 + 1 + 2
2 + 2
1 + 1 + 1 + 1
So the number of partitions of N = 4 is 5 partitions.
An excellent article of how to compute the partitions is contained on this page
The answer is 17977.
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1 solution
We need to compute the number of partitions of 36. There is no easy way to compute this number. There is a recurrence relation relating generalized pentagonal numbers with partition numbers, but there is an easier way to find the solution: the internet .