[seqfan] Re: Gen. Functs. A039219

[franktaw at netscape.net]

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