Padovan Hybrid Quaternions and Some Properties

Abstract

We define Padovan hybrid quaternions by using Padovan hybrid numbers and Padovan quaternion. We give the basic operation properties of Padovan hybrid quaternion numbers. We give some properties and identities such as the Binet formula, sum formula, the matrix representation, characteristic equation, norm, characteristic and generating function for these quaternions.

ON THE (p,q)-NARAYANA n-DIMENSIONAL RECURRENCES

“…The fourth-dimensional recurrences of the Narayana sequence are called quaternions. Similar studies can be found in [13][14][15][16][17][18].…”

Pascal's connection and fractions containing successive Padovan numbers in their decimal representation, reading left to right

“…The Padovan sequence is named after Richard Padovan who attributed its discovery to Dutch architect Hans van der Laan in his 1994 essay Dom and later were studied by many researchers [9,10,11]. This is sequence A000931 on the On-Line Encyclopedia of Integer Sequences (OEIS) [8].…”