[seqfan] Re: Gen. Functs. A039219
franktaw at netscape.net
franktaw at netscape.net
Tue Sep 15 23:55:36 CEST 2009
Actually, it's looking like this wasn't such a big problem as it
originally appeared to be. Other than the original base-related
sequences we first saw, almost all the errors are missing factors of x
(or a small power of x) or duplication of existing g.f.s.
And, unfortunately, there are quite a few g.f.s in the OEIS that are
off by a factor of x or x^2 or so. I fix these when I see them, but a
review of all the g.f.s in the database is not a realistic possibility.
And as for duplication of formulas, g.f.s or otherwise ...; well, part
of the problem is to decide just what constitutes a duplication.
For example, consider the triangular numbers (A000217). Leaving aside
that the first formula line is duplicated 7 lines down, we have both
a(n)+a(n+1) = (n+1)^2 and a(n) = (n+1)^2 - a(n+1) -- plus the comment
"Each pair of neighboring terms adds to a perfect square". Then there
are both a(n) = floor((2n+1)^2/8) and (2n+1)^2=8*a(n)+1; plus a comment
(sic) "(sqrt(8 a(n) + 1) - 1)/2 = n". (This isn't the only comment
that belongs in the formula section.) And the comment "Triangular
numbers - odd numbers = triangular numbers ..." essentially duplicates
the formula a(n) = a(n-2)+2n-1. There are probably more that I've
overlooked.
Franklin T. Adams-Watters
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