Chapter 40-Discriminants and the Element Sequence

Chapter40

Every linear integer sequence of a cubic polynomial has an associated element sequence.  The element sequence is the first derivative of the parent polynomial and easily obtained from its inter sequence polynomial.  Some sequences such as the Perrin sequence have an element sequence (the Padovan sequence) which is linearly proportional after rounding to its parent sequence.  This chapter discusses a method for finding this associated constant of proportion for any linear integer sequence based on the discriminant.  It is found that not all sequences exhibit this proportionality and an attempt is made to find condition for existence.

Discriminants and the Element Sequence