[seqfan] Re: Typo in formula-section of A001541 ?

[Richard Mathar]

ri> Robert Israel israel at math.ubc.ca
ri> Mon Mar 9 04:03:20 CET 2009
ri>...
ri> What's puzzling to me about A001541 is the statement in the "MAPLE" 
ri> section
ri> 
ri> A001541:=-(-1+3*z)/(1-6*z+z**2); [Conjectured by S. Plouffe in his 1992 
ri> dissertation.]
ri> 
ri> Presumably that's talking about the generating function.  But why was it
ri> only "conjectured", when it's very easy to prove (and is already stated
ri> as fact in the "Formula" section)?
....

There is a group of sequences with conjectured g.f.'s still to be put
on the "good" or "bad" side, which are not "trivial" in the sense that there
is no obvious recurrence and that the sequences are not known to sufficient
length which allow a simple test for a range of terms beyond the total order
of the numerator and denominator polynomials. Take for example:

A006172: this requires access to an article in the Fib Quarterly (which I
         do not have).

A006186: this requires access to an article to Ars Combin (1981) which I do
         not have.

A006071: this requires access to a book by Gardner, dto.

A005822: refers to an article in the Fib Quarterly

Everybody having these articles available could take a deeper look at them.

RJM