Question: combstruct: counting over a range

@Carl Love  Thanks for your reply. Composition breaks down into  distinct ordered  k-tuples . Partition breaks down into all possible sums with no regard to order.

Example: composition (4, 2)    {[1,3], [2,2], [3, 1]}   allstructs (Partition (4) ,size = 2)     [ [1, 3], [2,2]] 

For the allstructs ( Partition (n) , size = k ) command , I am trying to find out if there is command allowing me to define k not only as a single integer but a range of integers ( which should give me the sum of partitions of sizes over the defined range) . The maple help desk ( tech) advised me that there is no such command in the library. A programming procedure must be developed . And I am at minus infinity when it comes to programming! When I deal with small numbers, then it is relatively easy but also cumbersome to count. If we deal with large numbers then it is disruptive.

Thanks again for your time