figurate numbers
The sequence of numbers generated by counting the number of dots needed to construct the successive members of a specified n-gon.

For example, dots arranged in a series of regular triangular shapes can generate the sequence {1, 3, 6, 10, 15, . . .} while dots arranged in a series of squares can produce the sequence {1, 4, 9, 16, 25, . . .}.



 
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