[seqfan] Re: Another surprising omission from OEIS
William Keith
wjk26 at drexel.edu
Wed Nov 11 22:43:53 CET 2009
Chris Starling wrote:I just experimented by searching for some of my own sequences, with and
> without including a fake zero term. Including the fake zero did indeed
> throw a legitimate answer right out of the results. I don't mean off to the
> second page, but completely out.
Right; including the zero in the search string narrows the results to only sequences that include the zero. Including the zero in the submitted sequence returns hits for subsequences that include the zero and those that don't. If it makes sense by any reasonable definition, a zero term should be included.
Someone familiar with the OEIS will generally not include zero in a search string, because the utility of a returned result with a prepended zero is practically the same as that of one without. So since there is little cost to prepending a zero when it makes some sense, and a definite degradation of possible results when not prepending, I would suggest that we do.
Finally, there is the point that we do include a term for n=0 in most sequences, because this is the constant term of the related power series. We say there is 1 empty partition of 0 since this falls naturally out of the product form for the generating function. When in doubt, I suggest adding the 0 term.
William Keith
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