Wikipedia / Padovan polynomials
Wikipedia / 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 Pn−3(x) at x=1.
Evaluating Pn−3(x) at x=2 gives the nth Fibonacci number plus (−1)n.
The ordinary generating function for the sequence is