Talk:Padovan polynomials

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At the moment the general recurrence given in this article is:

P_n(x) = xP_{n − 2}(x) + P_{n − 3}(x)

which gives two Padovan polynomials with degree 2, two with degree 3 etc. Why is the recurrence not

P_n(x) = x²P_{n − 2}(x) + xP_{n − 3}(x)

so that P_n(x) always has degree n-1, and there is a only one Padovan polynomial with a given degree ? This would be a closer analogue to Fibonacci polynomials. Gandalf61 11:21, August 26, 2005 (UTC)