On 8/22/10, N. J. A. Sloane <njas@research.att.com> wrote:
Fred Lunnon said:
I fed A180238 to gfun via Maple9 --- and strange to say, gfun replied straight away "FAIL". So as I suspected, it is nonsense; and there appear to be bugs both in the way superseeker is to utilising the gfun package, and its output of the results; while the documentation leaves something to be desired (like, some documentation)!
Superseeker would say that WFL was not familiar with gfun, which has a lot of commands.
With which WFL would be the first to agree. However ...
Look:
s1:=[1,3,9,27,75,189,447,951,1911,3621];
(that is A180238)
listtoalgeq(s1,y(x),[lgdegf]); 2 3 [-27 + 27 y(x) - 9 y(x) + y(x) , lgdegf]
The result may be nonsense, but Superseeker feels an obligation to report it, since once in a while it finds useful things.
Fair enough. But just allow me point out two subtle differences --- (1) NJAS explicitly calls "listtoalgeq()", allowing anyone with access to gfun commands to deduce that the output will be an equation defining an algebraic generating function. (2) NJAS uses as his variable y(x). Not a(n), as reserved elsewhere for terms of the original sequence. As a result, NJAS's demonstration is informative, whereas superseeker's output is --- in this case --- quite unnecessarily baffling.
As for documentation, the help file (send an empty email to superseeker@research.att.com) describes what it does. It states that it uses gfun, but of course does not show the large set of descriptions of all the gfun commands.
Descriptions are not needed --- even just a trace citation would help, as already provided via "lgdegf" etc (the latter being further enhanced with one-line definitions in a footnote).
And as I said earlier the full Superseeker code can be seen on the OEIS web site.
Best regards Neil
PS The web page cite.html (on the OEIS site) mentions quite a few results that were found with the aid of Superseeker.
Not this time round, alas --- the only solution of (y(x) - 3)^3 = 0 is y = 3; and the Taylor coefficients of exp(3 x) are obviously small and non-integer. So the nonsense originates with gfun; but I call attention to the fact that neither gfun nor superseeker seems to have checked the result against the input and suppressed it. Irrespective of superseeker's impressive record of successes, both these situations could surely be improved. Incidentally, I don't feel too bad about the wasted time, this time round --- I didn't know about gfun before, and it does look potentially useful. Fred Lunnon