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%I #31 Mar 19 2020 14:51:50
%S 1,1,1,3,6,197,3684,159561
%N a(n) is the number of distinct absolute values of 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 calculated the determinants. We then obtained the absolute values of the determinants and removed duplicates.
%C These results are based on work supported by the National Science Foundation under grants numbered DMS-1852378 and DMS-1560019.
%C a(9) >= 1747706. - _Hugo Pfoertner_, Nov 20 2019
%H Froylan Maldonado, <a href="/A309258/a309258.sage.txt">Code</a>
%H Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/data/latin.html">Latin squares</a>
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a309258.pdf">8X8 Latin squares: Illustration of occurrence counts of determinant values</a>, 5.7 MB, zoom in to see details (2019).
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a309258.zip">Occurrence counts of determinant values for n=1..8</a>, zipped (2019).
%e For n = 5, the set of absolute values of determinants is {75, 825, 1200, 1575, 1875, 2325}, so a(5) = 6.
%o (Sage) # See Maldonado link.
%Y Cf. A040082, A088021, A301371, A308853, A309984, A309985.
%K nonn,hard,more
%O 1,4
%A _Alvaro R. Belmonte_, _Eugene Fiorini_, _Peterson Lenard_, _Froylan Maldonado_, _Sabrina Traver_, _Wing Hong Tony Wong_, Jul 19 2019
%E a(8) from _Hugo Pfoertner_, Aug 26 2019
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