Catalan Transformation of (s; t) Padovan Sequences

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Published: 2023-05-22

Page: 170-178


. Priyanka

Srinivasa Ramanujan Department of Mathematics, Central University of Himachal Pradesh, Dharamshala(HP)-176215, India.

Shilpa Kapoor *

Srinivasa Ramanujan Department of Mathematics, Central University of Himachal Pradesh, Dharamshala(HP)-176215, India.

Pankaj Kumar

Srinivasa Ramanujan Department of Mathematics, Central University of Himachal Pradesh, Dharamshala(HP)-176215, India.

*Author to whom correspondence should be addressed.


Abstract

The objective of this research is to introduce the Catalan transform of (s; t) Padovan sequence {CP(s;t),m}(m\(\geq\)0). It is proved that the Catalan transform of (s; t) Padovan sequence {CP(s;t),m}(m\(\geq\)0) is the product of the Catalan matrix and the matrix of the (s; t) Padovan sequence (which is nx1 matrix). In addition to this, the generating function of the newly generated Catalan transformation of (s; t) Padovan sequence is formed, and then the Hankel Transform of Catalan transformation of (s; t) Padovan sequence is also calculated by the determinant of the matrix obtained from (s; t) Padovan sequence {P(s;t),m}(m\(\geq\)0).

Keywords: Padovan sequence, Catalan transform, Hankel transform


How to Cite

Priyanka, ., Kapoor, S., & Kumar, P. (2023). Catalan Transformation of (s; t) Padovan Sequences. Asian Journal of Pure and Applied Mathematics, 5(1), 170–178. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1812

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