[seqfan] Re: 448 ways

[Neil Sloane]

Could the explanation (why on earth would someone say "nonnegative
square"?)
be that they meant to say "nonzero sequence"?  It's not a typo, it's a
braino.    So the fix would be to replace
"nonnegative square" with "nonzero square" ??

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 Sat, Nov 18, 2017 at 12:10 PM, Peter Munn <techsubs at pearceneptune.co.uk>
wrote:

> Dear seqfans,
>
> On Thu, November 16, 2017 6:09 pm, Allan Wechsler wrote:
> > Very interesting! So we need a new sequence, "numbers N for which no K
> is
> > the sum of five squares in exactly N ways", of which 448 will be the
> leading entry.
>
> Another sequence in which 448 would be the first term is "least m for
> which no K is the sum of n squares in exactly m ways", which would have an
> offset for n of 5.  Maybe it would be easier to calculate sufficient terms
> for this?
>
> By the way, how do others see the "nonnegative" qualification for "square"
> in the name of A295159?
>
> 19 sequences showed up in the OEIS search as having "nonnegative square"
> in their name (when excluding those also having "root" in the name), but
> only 7 of them date from before this month.
>
> Four of these, A229062, A073613, A160053 and A180161, do so with clear
> reference to A001481, which no longer has the qualification in its own
> name, "Numbers that are the sum of 2 squares."  Another, A230314, "Numbers
> that are simultaneously the sum of two nonnegative squares and the sum of
> two nonnegative cubes", benefits by pointing out a symmetry.
>
> Of the remaining two, A006431, "Numbers that have a unique partition into
> a sum of four nonnegative squares" is clearly the one related to A295159.
> The other, A166498, has had its "nonnegative" deleted following my
> questioning it when making a correction.
>
> Best Regards,
>  Peter Munn
> > On Thu, Nov 16, 2017 at 7:14 AM, Giovanni Resta
> > <giovanni.resta at iit.cnr.it>
> > wrote:
> >> On 11/16/2017 03:51 AM, israel at math.ubc.ca wrote:
> >> To make that lower bound 448 would require x >= 2339578, and that's too
> >>> big for me to search. But maybe better lower bounds are known.
> >> I checked all the x between 25000 and 2339600 and all have at least 449
> decompositions as a sum of five squares.
> >> Giovanni
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>
>
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>
>
>
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