function to generate collections of integers that all sum to the same value?

Here's one for you number freaks.I am looking for a Matlab function that generates all ordered combinations of integers that add up to a certain value. For instance, in the case of 4,

1 1 1 1

1 1 2, 1 2 1, 2 1 1

1 3, 3 1

2 2

4

In the case of 5,

1 1 1 1 1

1 1 1 2, 1 1 2 1, 1 2 1 1, 2 1 1 1

1 2 2, 2 1 2, 2 2 1

1 1 3, 1 3 1, 3 1 1

1 4, 4 1

2 3, 3 2

5

Etc., all the way up to 8, or even 16 if that is possible.

Answer 1

[Bruno Luong]

Look in File Exchange with the keywords integer partition. You'ill find many implementations for example this one:

https://www.mathworks.com/matlabcentral/fileexchange/36437-integer-partition-generator?s_tid=srchtitle

[mark palmer]

Thanks, I didn't realize this was a common question.

[John D'Errico]

Be careful, as even relatively small numbers will have an immense number of partitions. By my count, 100 has 190569292 distinct ways to perform the sum, and 1000 has 24061467864032622473692149727991 distinct ways.