We study some sequences of multi-polygonal numbers, specifically the square triangular, oblong triangular, pentagonal triangular, and pentagonal square numbers. To do so, we state and prove theorems that relate the factors of a given triangular number to a pair of larger triangular numbers with a triangular sum, and relate a triangular number that is three times another triangular number (or three times a square) to a larger pair of triangular numbers with the same property.
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