[seqfan] Re: Typo in formula-section of A001541 ?
Robert Israel
israel at math.ubc.ca
Mon Mar 9 04:03:20 CET 2009
Of course you're right, as is obvious from the fomula
a(n) = ((3+2*sqrt(2))^n + (3-2*sqrt(2))^n)/2.
What's puzzling to me about A001541 is the statement in the "MAPLE"
section
A001541:=-(-1+3*z)/(1-6*z+z**2); [Conjectured by S. Plouffe in his 1992
dissertation.]
Presumably that's talking about the generating function. But why was it
only "conjectured", when it's very easy to prove (and is already stated
as fact in the "Formula" section)?
Cheers,
Robert Israel
On Mon, 9 Mar 2009, Peter Pein wrote:
> The sixth entry in the formulas for
> http://www.research.att.com/~njas/sequences/A001541 reads:
>
> "For all elements x of the sequence, 2*x^2 - 2 is a square. Lim. as n -> inf.
> of a(n)/a(n-1) = 3 + sqrt(2). - Gregory V. Richardson (omomom(AT)hotmail.com),
> Oct 10 2002"
>
> but the lim_{n->oo}{a(n)/a(n-1)} is 3 + 2 sqrt(2).
> ^
>
> Or did I (again) misinterpret anything?
>
> Peter
>
>
>
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