%I #22 Mar 14 2020 17:21:54
%S 1,3,18,80,75,63,196,144,405
%N a(n) is the greatest common divisor of the determinants of order n Latin squares.
%C 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.
%C These results are based upon work supported by the National Science Foundation under the grants numbered DMS-1852378 and DMS-1560019.
%H Peterson Lenard, <a href="/A309259/a309259.sage.txt">Greatest Common Divisor of all determinants</a>
%H Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/data/latin.html">Combinatorial Data</a>
%e 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.
%o (Sage) # See Peterson Lenard link
%Y Cf. A301371, A308853, A309088, A309258.
%K nonn,hard,more
%O 1,2
%A _Alvaro R. Belmonte_,_Eugene Fiorini__,_Peterson Lenard_, _Froylan Maldonado_, _Sabrina Traver_, _Wing Hong Tony Wong_, Jul 19 2019
%E a(8), a(9) from _Hugo Pfoertner_, Sep 02 2019