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.
vectorization in N
Equal to their cube
Length of the hypotenuse
Maintain shape of logical-index mask
Cull vector elements that contain a specified digit
Is my wife right? Now with even more wrong husband
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