figurate number

noun

: any of a progression of numbers formed from an arithmetical progression in which the first term is 1 and the difference an integer by taking the first term, and the sums of the first two, first three, first four, and so on as the successive terms of a new progression and by operating on this in the same way, and so on, the numbers in each sequence being such that points representing them are capable of arrangement in geometrical figures

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