Catalan Transformation of (s; t) Padovan Sequences
. 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