[seqfan] Re: A132870 : a Mathematica line

Marc LeBrun mlb at well.com
Mon Nov 20 20:19:54 CET 2017


Wouldn't it be nicer to have two sequences, a numerator and a denominator?


> On Nov 20, 2017, at 10:44 AM, Neil Sloane <njasloane at gmail.com> wrote:
> 
> Since the triangle is integral for a long time, I think it is enough to
> leave the entry the way it is, but to make it clear in the comments that
> this stops being integral beyond a certain point.
> 
> There is a famous recurrence (discussed by Lenstra) which is integral for
> 48 or so terms but then isn;'t, and we handled that in the same way.  We
> pretend it is integral, but add a warning that it really isn't.
> And we stop the b-file before we hit the rocks.
> 
> 
> Best regards
> Neil
> 
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
> 
> 
> On Mon, Nov 20, 2017 at 12:47 PM, Paul Hanna <pauldhanna.math at gmail.com>
> wrote:
> 
>> Wouter,
>>      Thanks for verifying the fractional elements.
>> "Bummer" is right ...
>> I'll ask Neil what to do with the non-integral triangle.
>> Thank you!
>>      Paul
>> 
>> On Sat, Nov 18, 2017 at 11:50 AM, Wouter Meeussen <
>> wouter.meeussen at telenet.be> wrote:
>> 
>>> pt = {{1}}; Table[rhs = CoefficientList[(k^2 + x)^k, x];
>>> qt = Join[pt, {vars = Array[Subscript[a, #] &, k + 1]}];
>>> b = MatrixPower[PadRight[qt], k] ;
>>> {out} = vars /. Solve[Thread[Reverse[Last[b]] == Reverse[rhs]], vars];
>>> pt = Join[pt, {out}]; out, {k, 20}]
>>> 
>>> 
>>> not the fastest of codes : the first 20 rows take 43 seconds on my old
>>> machine.
>>> 
>>> 
>>> W.
>>> 
>>> --
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>> 
>> 
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>> 
> 
> --
> Seqfan Mailing list - http://list.seqfan.eu/




More information about the SeqFan mailing list