Generalized Padovan and polynomial sequences

Abstract

By generalizing the well-known classical Padovan Sequence using Quadratic, Cubic and general polynomial sequences as coefficients we arrive at various limiting ratios in this paper. Few illustrations are provided to justify the results arrived regarding the limiting ratios. The idea of limiting ratio will provide the asymptotic behavior of the terms of the sequence. In this sense, the results obtained in this paper will provide more information about the behavior of Padovan sequence in combination with general polynomial sequences.