Problem 44334. Sums of Multiple Pairs of Triangular Numbers

This is a follow-up to Problem 44289 - Find two triangular numbers whose sum is input.

There are some numbers that are the sum of multiple pairs of triangular numbers. For example, 81 = 36+45 = 15+66 = 3+78. Given a number X, find all of the possible pairs of triangular numbers that add up to X. Your answer should be in a 2-by-X matrix. Each column of the matrix should sum to X, and each pair of triangular numbers should only appear once. The top row sorted from low to high. The output for 81 would be:

 [ 3   15  36 
  78   66  45]

Good luck!