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 A008346 in the OEIS)

The ordinary generating function for the sequence is

See also

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References

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