Integer partition generator

Generates a table of all integer partitions of integers from 0 to N.

Integer partitions are the different ways to express an integer say "4" as a sum of other positive integers, in this case we would have 4=4,3+1,2+2,2+1+1,1+1+1+1. This program calculates all the partitions of every integer up to N which it stores in a cell array.

There is the option of only using partitions with up to "maxnum" integers, e.g. if maxnum = 3 the parition 1+1+1+1 (of 4) would be disallowed.

Also contained is a file to generate the number of integer partitions of an integer N using up to k integers which is used in the main file. Both files work via the recursive property of integer partitions and use integer class variables.

Update: Version two also allows the extra option of using only a restricted range of integers for the partition as well as a restricted number.

Example Useage:

Say I wanted to generate all the partitions of the numbers 0-100, using at most 6 numbers. Of which there are 3574454 this is calculated by:
table = integerparttable(100);
>> sum(table(:,7))

This set would be given by:
parts = intpartgen(100,6);
(Which takes ~ 20 seconds to compute on my machine.)

If I later wanted to extend this set to all the partitions up to 110, I can pass this list back to the function so it doesn't have to recalculate them all

parts = intpartgen(110,6,parts);

Note that parts{k+1} is the partitions of k (since arrays start from 1 and the partition for 0 is included as part{1})

To calculate the number of ways to pay a sum of money at most 10 coins
>>> intlist = intpartgen2(value,10,[],[0,1,2,5,10,20,50,100]);
>>> ways_to_pay = intlist{value+1};
(for exactly 10 coins remove the value zero from allowed numbers)