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A076021
Number of fully idempotent systems with n elements with one binary operation satisfying the equation B(AB)=A (idempotent semisymmetric quasigroups).
7
1, 0, 1, 1, 0, 0, 4, 0, 20, 241, 0, 9801188
OFFSET
1,7
COMMENTS
a(n) = 0 whenever n == 2 (mod 3).
a(n) is also the number of unipotent semisymmetric quasigroups of order n+1 and is also the number of semisymmetric loops of order n+1.
LINKS
Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Des. 30 (2022), 105-130.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Richard C. Schroeppel, Oct 29 2002
EXTENSIONS
a(10)-a(12) from Ian Wanless, Dec 08 2021
STATUS
approved