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A309259
a(n) is the greatest common divisor of the determinants of order n Latin squares.
1
1, 3, 18, 80, 75, 63, 196, 144, 405
OFFSET
1,2
COMMENTS
We apply every symbol permutation on the representatives of isotopic classes to generate Latin squares of order n and calculate the determinants. We then compute the greatest common divisor of the values obtained.
These results are based upon work supported by the National Science Foundation under the grants numbered DMS-1852378 and DMS-1560019.
EXAMPLE
For n=4, the set of absolute values of the determinants is {0, 80, 160}, so the greatest common divisor of the determinants is 80. Therefore, a(4)=80.
PROG
(Sage) # See Peterson Lenard link
CROSSREFS
KEYWORD
nonn,hard,more
EXTENSIONS
a(8), a(9) from Hugo Pfoertner, Sep 02 2019
STATUS
approved