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Number of isotopism classes containing symmetric unipotent reduced Latin squares of order 2n.
2

%I #13 Dec 10 2021 11:09:11

%S 1,1,1,6,396,526915616,1132835421602062347

%N Number of isotopism classes containing symmetric unipotent reduced Latin squares of order 2n.

%C Isotopism classes are obtained by permuting rows, permuting columns and permuting symbols. There is a stronger notion of equivalence called "species" (also known as main classes and paratopism classes). For this particular problem the counts for species equal the counts for isotopism classes.

%H Brendan D. McKay and Ian M. Wanless, <a href="https://doi.org/10.1002/jcd.21814">Enumeration of Latin squares with conjugate symmetry</a>, J. Combin. Des. 30 (2022), 105-130.

%Y For odd n the terms equal A000474.

%Y Cf. A350009.

%K nonn,more

%O 1,4

%A _Ian Wanless_, Dec 08 2021