Check whether the input matrix is a figurate number triangle: http://mathworld.wolfram.com/FigurateNumberTriangle.html
you should probably add a test case where the correct answer is false.
I added a few more tests as suggested.
The Goldbach Conjecture
Is this matrix orthogonal?
Change the sign of even index entries of the reversed vector
So many choices
All your base are belong to us
Cull vector elements that contain a specified digit
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