You should be a bit more ambitious and apply the number wall algorithm to find identify general linear recurrences. Polynomials would fall out as a special case, as would polynomials with a few rogue initial elements, and interleaved polynomials.

-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Keith F. Lynch Sent: Saturday, November 03, 2018 11:51 PM To: math-fun@mailman.xmission.com Subject: Re: [math-fun] Finding a polynomial from an integer sequence

Thanks to everyone who responded to my query, especially Tomas Rokicki, who described a matrix method for the specific problem I was interested in, and Rich Schroeppel, who described a way that will work for any sequence, including one with terms missing.

Of course any finite subsequence of an infinite sequence will match an unlimited number of polynomials, and there doesn't seem to be any way of telling which, if any, is correct. If the order of a polynomial is much less than the number of terms, that's evidence, but not proof, that that polynomial is correct.

I'm tempted to test every sequence in OEIS to see if it appears to be polynomial, and if not, to see if it can be made polynomial by altering, removing, or interpolating one element. If it can be, it might be that I've found an error in the sequence, or at least an oddity that could do with some exploration. Has anyone done this already? Thanks.

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