### Journals Information

**
Mathematics and Statistics Vol. 11(3), pp. 454 - 463 DOI: 10.13189/ms.2023.110303 Reprint (PDF) (819Kb) **

## Historical Review of Existing Sequences and the Representation of the Wing Sequence

**Maizon Mohd Darus ^{1}^{,*}, Haslinda Ibrahim ^{2}, Sharmila Karim ^{2}**

^{1}Centre of Foundation and Language Studies, Limkokwing University of Creative Technology, Jalan Teknokrat 1/1, 63000 Cyberjaya, Selangor, Malaysia

^{2}Department of Mathematics, School of Quantitative Sciences, Universiti Utara Malaysia, Changlun, 06010 Sintok, Kedah, Malaysia

**ABSTRACT**

A sequence is simply an ordered list of numbers. Sequences exist in mathematics very often. The Fibonacci, Lucas, Perrin, Catalan, and Motzkin sequences are a few that have drawn academics' attention over the years. These sequences have arisen from different perspectives. By investigating the construction of each sequence, these sequences can be classified into three groups, i.e., those that arise from nature, are constructed from other existing sequences, or are generated from geometric representation. This outcome may assist the researchers in adding a new number sequence to the family of sequences. Our observation of the geometric representation of the Motzkin sequence shows that a new sequence can be constructed, namely the Wing sequence. Therefore, we demonstrate the iterations of the Wing sequence for 3≤n≤5. The wings are constructed by classifying them into (n-1) classes and determining the first and second points. It will then provide (n-2) wings in each class. This technique will construct (n-1)(n-2) wings for each n. The iterations may provide a basic technique for researchers to construct a sequence using the technique of geometric representation. The observation of geometric representations can develop people's thinking skills and increase their visual abilities. Hence, the study of geometric representation may lead to new lines of research that go beyond only sequences.

**KEYWORDS**

Motzkin, Wing Sequence, Geometric Representation

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Maizon Mohd Darus , Haslinda Ibrahim , Sharmila Karim , "Historical Review of Existing Sequences and the Representation of the Wing Sequence," Mathematics and Statistics, Vol. 11, No. 3, pp. 454 - 463, 2023. DOI: 10.13189/ms.2023.110303.

(b). APA Format:

Maizon Mohd Darus , Haslinda Ibrahim , Sharmila Karim (2023). Historical Review of Existing Sequences and the Representation of the Wing Sequence. Mathematics and Statistics, 11(3), 454 - 463. DOI: 10.13189/ms.2023.110303.