Padovan polynomials

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 P"n"−3("x") at "x" = 1.
Evaluating P"n"−3("x") at "x" = 2 gives the "n"th Fibonacci number plus (−1)"n". 
The ordinary generating function for the sequence is