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A309089 a(n) is the number of absolute values of determinants that come from a unique isotopy class of order n Latin squares.

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%I A309089 #19 Apr 09 2020 21:39:33
%S A309089 1,1,1,2,5,85,124
%N A309089 a(n) is the number of absolute values of determinants that come from a unique isotopy class of order n Latin squares.
%C A309089 We apply every symbol permutation on the representatives of isotopic classes to generate Latin square of order n and calculate the determinants.
%C A309089 These results are based upon work supported by the National Science Foundation under the grants numbered DMS-1852378 and DMS-1560019.
%H A309089 Peterson Lenard, <a href="/A309089/a309089.sage.txt">Number of unique determinants</a>
%H A309089 Brendan McKay, <a href="https://users.cecs.anu.edu.au/~bdm/data/latin.html">Latin squares</a>
%e A309089 For n=4, the determinants 80 and 160 are produced by a unique isotopic class which has [[1, 2, 3, 4], [2, 4, 1, 3], [3, 1, 4, 2], [4, 3, 2, 1]] as a representative. All other determinants are produced by multiple isotopic classes. Therefore a(4)=2.
%o A309089 (Sage) # See Maldonado link
%Y A309089 Cf. A301371, A308853, A309088.
%K A309089 nonn,hard,more
%O A309089 1,4
%A A309089 _Alvaro R. Belmonte_, _Eugene Fiorini__, _Peterson Lenard_, _Froylan Maldonado_, _Sabrina Traver_, _Wing Hong Tony Wong_, Jul 11 2019