[seqfan] Re: 448 ways

[Peter Munn]

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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