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.
Find state names that start with the letter N
Side of an equilateral triangle
So many choices
Sum my indices
Maintain shape of logical-index mask
Increment a number, given its digits
The Hitchhiker's Guide to MATLAB
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