(s1,s2)-Padovan matrix sequence and the case of generalization

Abstract

In this work we present the (s, t)-Padovan matrix sequence generalization by means of (s1, s2, s3)-Tridovan matrix sequence definition. The first one studied primarily by [5] as (s, t)-Padovan matrix sequence, where s and t are arbitraries integers coefficients, in this work we present a new matrix sequence definition for a generic number of integer coefficients, denominated from now on as (s1, s2, . . . , sz)-Z-dovan. In addition the (s1, s2, s3)-Tridovan matrix sequence is presented. In general, one can note that the Padovan or Cordonnier sequence is a particular case of this generalized matrix sequence. A study along this linear, recurrent and recursive sequence is carried out in order to support new definitions, theorems and other studies with a consolidated theoretical foundation.