Number of distinct arrays

[hamidgasmi]

Given a sum of positive integers S and a their number n, find the number of distinct arrays under these conditions:

• In each array, there are n elements whose sum is equal to S.

• In each array, each element should be greater than or equal to the element on its left.

• The elements formed in each array are distinct

• E.g. 1.:

  • Inputs: S = 8 n = 4
  • Output: 5
  • Explanation: [1,1,1,5], [1,1,2,4], [1,1,3,3], [1,2,2,3], [2,2,2,2]
  • Each array has 4 (n) elements a sum of 8 (S) with each element on the left <= element on the right. There are 5 possible distinct options.