A computer-based approach in generating the Catalan sequence and some applications

• Main Authors: Perez, Marinea C., Atilon, Lawrence B.
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Sequences (Mathematics); Programming (Mathematics); Computer software; Trees (Graph theory); Numbers, Real
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16452
• Institution: De La Salle University

This thesis is an exposition of different methods in generating the Catalan Sequence and some applications. Applications include r. some graph theory and getting the total number of possible sets given a certain condition. Methods and applications (except the r) were obtained from two articles from the mathematical magazine ([2], [3]) and one previous thesis ([1]). In these two articles, no proof was given in order to validate these applications but through the illustrations of the researchers, we concluded that the applications really generate the Catalan numbers. Another article showed the relationship between the Catalan sequence and 4 [4]. The researchers have provided a detailed proof because the proof in the article was not elaborated. While this research, the researchers saw the need to develop a software in generating the Catalan sequence because the terms increase rapidly and therefore manual computation may be difficult since you have to deal with very large numbers. It was also developed to get accurate and precise numbers because calculators do not gives accurate and precise numbers. The software was written in Turbo Pascal 7.0 language and DOS environment and it has its limitatios due to lack of time to learn another language and unavailability of resources.