On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers

Somphong Jitman and Chakrit Phongthai

International Journal of Mathematics and Mathematical Sciences, 2017, vol. 2017, 1-6

Abstract:

A trapezoidal number, a sum of at least two consecutive positive integers, is a figurate number that can be represented by points rearranged in the plane as a trapezoid. Such numbers have been of interest and extensively studied. In this paper, a generalization of trapezoidal numbers has been introduced. For each positive integer , a positive integer is called an - trapezoidal number if can be written as an arithmetic series of at least terms with common difference . Properties of -trapezoidal numbers have been studied together with their trapezoidal representations. In the special case where , the characterization and enumeration of such numbers have been given as well as illustrative examples. Precisely, for a fixed -trapezoidal number , the ways and the number of ways to write as an arithmetic series with common difference have been determined. Some remarks on -trapezoidal numbers have been provided as well.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:4515249

DOI: 10.1155/2017/4515249

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