The first test case is wrong 0 and 21 are triangular numbers too (https://oeis.org/A000217), therefore:
[ 0, 6;
PS: And 0 does not make a pair with every number in this case.
What's wrong with the case x=20 in test suite? Why is y_correct=[ 10 10] ? I cannot pass it.
I don't know why your cheat isn't working, but look closely at what numbers your "for n=1:N" loop generates for that case.
Word Counting and Indexing
Project Euler: Problem 4, Palindromic numbers
Matrix indexing with two vectors of indices
Remove element(s) from cell array
MATLAB Basic: rounding IV
Muphry's Law of MATLAB
Some Assembly Required
Crunch that matrix!
Don't be mean. Be nice!
Sums of Distinct Powers
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