Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed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 (doi: 10.20944/preprints202102.0385.v2). Adegoke, K. Basic Properties of the Polygonal Sequence. Preprints 2021, 2021020385 (doi: 10.20944/preprints202102.0385.v2).

Abstract

We study various properties of the polygonal numbers; such as their recurrence relations, fundamental identities, weighted binomial and ordinary sums and the partial sums and generating functions of their powers. 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 as is the case in most literature.

Keywords

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

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comments (1)

Comment 1
Received: 24 February 2021
Commenter: Kunle Adegoke
Commenter's Conflict of Interests: Author
Comment: Added more results.
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