Padovan polynomials (original) (raw)

In mathematics, Padovan polynomials are a generalization of Padovan sequence numbers. These polynomials are defined by: The first few Padovan polynomials are: The Padovan numbers are recovered by evaluating the polynomials Pn−3(x) at x = 1. Evaluating Pn−3(x) at x = 2 gives the nth Fibonacci number plus (−1)n. (sequence in the OEIS) The ordinary generating function for the sequence is