[seqfan] Re: Q about magic squares as produced by Matlab

[Neil Sloane]

Robert, Thanks - that explains everything. I'll follow your advice and
change the definition

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 Tue, Oct 27, 2015 at 6:59 PM, <israel at math.ubc.ca> wrote:

> This is a known issue with Matlab's "magic". The Matlab help file for
> magic states:
>
> -----------------------------
> M = magic(n) returns an n-by-n matrix
> constructed from the integers 1 through n^2 with
> equal row and column sums. The order n must be a scalar greater than
> or equal to 3.
>
> ...
>
> Limitations
> If you supply n less than 3, magic returns
> either a nonmagic square, or else the degenerate magic squares 1 and [].
> ---------------------------------
>
> In fact magic(2) returns the matrix
>
> [ 1 3 ]
> [ 4 2 ]
>
> which does have determinant -10.
>
> I guess we could insert the value -10, changing the Name to "a(n) is the
> determinant of the matrix returned by the Matlab
> command magic(n)", with a comment to the effect that for n=2 this
> is not a magic square.  Or delete the 1 (on the grounds that Matlab
> says n must be >= 3) and make the offset 3.
>
> Cheers,
> Robert
>
>
> On Oct 27 2015, Neil Sloane wrote:
>
> Dear Seqfans, Sequence A160523 is
>> a(n) is the determinant of the magic square of order n produced by Matlab.
>> 1, -360, 0, 5070000, 0, -348052801600
>> Offset 1 (which must be wrong)
>> (Matlab) det(magic(n));
>>
>> I just received an email from someone saying:
>>
>> "det(magic(2)) = -10 and maybe a(2) should be added the sequence."
>>
>> and giving the matrix
>> 1 3
>>
>> 4 2
>>
>> - which of course is not a magic square of order 2. There are no magic
>> squares of order 2. But maybe Matlab thinks there are.
>>
>> There is clearly something wrong with A160253.
>>
>> Could someone who has access to Matlab kindly check it?
>>
>>
>> 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
>>
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