

A076016


Number of systems with n elements having one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups).


7



1, 2, 3, 18, 120, 2880, 140256, 20782080, 9569532672, 14175610675200, 74559788174868480
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Or, Latin squares for which the set of (row,column,symbol) triples is invariant under cyclic permutation of the elements within each triple.


LINKS

Table of n, a(n) for n=1..11.
Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Des. 30 (2022), 105130.


CROSSREFS

Cf. A076017A076021, A350019, A350020.
Sequence in context: A166510 A288492 A184719 * A226961 A107095 A102939
Adjacent sequences: A076013 A076014 A076015 * A076017 A076018 A076019


KEYWORD

nonn,hard,more


AUTHOR

Richard C. Schroeppel, Oct 29 2002


EXTENSIONS

a(10)a(11) from Ian Wanless, Dec 08 2021


STATUS

approved



