On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers
Joint Authors
Jitman, Somphong
Phongthai, Chakrit
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-08-22
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
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 m, a positive integer N is called an m-trapezoidal number if N can be written as an arithmetic series of at least 2 terms with common difference m.
Properties of m-trapezoidal numbers have been studied together with their trapezoidal representations.
In the special case where m=2, the characterization and enumeration of such numbers have been given as well as illustrative examples.
Precisely, for a fixed 2-trapezoidal number N, the ways and the number of ways to write N as an arithmetic series with common difference 2 have been determined.
Some remarks on 3-trapezoidal numbers have been provided as well.
American Psychological Association (APA)
Jitman, Somphong& Phongthai, Chakrit. 2017. On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers. International Journal of Mathematics and Mathematical Sciences،Vol. 2017, no. 2017, pp.1-6.
https://search.emarefa.net/detail/BIM-1167726
Modern Language Association (MLA)
Jitman, Somphong& Phongthai, Chakrit. On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers. International Journal of Mathematics and Mathematical Sciences No. 2017 (2017), pp.1-6.
https://search.emarefa.net/detail/BIM-1167726
American Medical Association (AMA)
Jitman, Somphong& Phongthai, Chakrit. On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers. International Journal of Mathematics and Mathematical Sciences. 2017. Vol. 2017, no. 2017, pp.1-6.
https://search.emarefa.net/detail/BIM-1167726
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1167726