A summing problem

[Sarad AV]

hi,

there is a positive integer n and i am trying to
device an algorithm that gives me all the possible
summation combinations.

For e.g.
n=4

1+3=4
2+2=4
1+1+1+1=4
1+2+1=4

The ordering is not important. Hence there are 4
possible summation combinations.

All attempts to make an algorithm gives exponential
time solutions. Is there a polynomial time solution to
it?

Given n, is there a formula that would count all its
existing summations?

Thank you,
Sarad.


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