Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

Basic Properties of the Polygonal Sequence

Version 1 : Received: 17 February 2021 / Approved: 17 February 2021 / Online: 17 February 2021 (12:06:12 CET)
Version 2 : Received: 24 February 2021 / Approved: 24 February 2021 / Online: 24 February 2021 (10:29:09 CET)
Version 3 : Received: 25 February 2021 / Approved: 26 February 2021 / Online: 26 February 2021 (09:21:39 CET)

How to cite: Adegoke, K. Basic Properties of the Polygonal Sequence. Preprints 2021, 2021020385. Adegoke, K. Basic Properties of the Polygonal Sequence. Preprints 2021, 2021020385.


We study various properties of the polygonal numbers; such as their recurrence relations; fundamental identities; weighted binomial and ordinary sums; partial sums and generating functions of their powers; and a continued fraction representation for them. A feature of our results is that they are presented naturally in terms of the polygonal numbers themselves and not in terms of arbitrary integers; unlike what obtains in most literature.


polygonal number; triangular number; summation identity; generating function; partial sum; recurrence relation


Computer Science and Mathematics, Algebra and Number Theory

Comments (1)

Comment 1
Received: 26 February 2021
Commenter: Kunle Adegoke
Commenter's Conflict of Interests: Author
Comment: Added more results.
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