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Numbers Simultaneously Polygonal and Centered Polygonal

Steven J. Schlicker
Mathematics Magazine
Vol. 84, No. 5 (December 2011), pp. 339-350
DOI: 10.4169/math.mag.84.5.339
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Page Count: 12
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Numbers Simultaneously Polygonal and Centered Polygonal
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Summary The study of polygonal numbers (triangular, square, etc.) has a long and rich history. Similar, but lesser known, are the centered polygonal numbers which have not been as extensively studied. These sequences of figurate numbers contain a wealth of interesting and fun mathematics. As an example, we make connections between the polygonal and centered polygonal numbers to find a previously unknown family of integer sequences that describe those numbers that are simultaneously polygonal and centered polygonal for the same number of sides.

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