Find combinations of non-repeating integers summing to a certain number

Given a number x, I would like to find all non-repeating combinations of integers in range 1:n that form a vector of length m whose elements sum to x.

For example: x = 9; n = 6; m = 3;

Should return: [4 3 2] [5 3 1] [6 2 1]

This will be used many times with an n ~ 100, and needs to be general for any x or m, so the method should be as efficient as possible.

Answer 1

[John D'Errico]

Using my partitions code...

partitions(9,1:6,1,3)
ans =
   0     1     1     1     0     0
   1     0     1     0     1     0
   1     1     0     0     0     1

A 1 in any row indicates that element appears in the sum.

For a larger problem, here are the set of all solutions with a sum of 100, 3 elements in the sum, from the set 1:60. 423 possible solutions.

sols = partitions(100,1:60,1,3);
size(sols)
ans =
   423    60

partitions can be found on the file exchange.

Of course, it is trivial to create an impossibly large problem, but partitions is reasonably efficient on rationally sized problems.

[Daniel]

This is exactly what I needed. Thanks!