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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..12.

Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Des. 30 (2022), 105-130.

CROSSREFS

Cf. A076016-A076020.

Sequence in context: A199933 A078630 A178671 * A179270 A246132 A229827

Adjacent sequences:  A076018 A076019 A076020 * A076022 A076023 A076024

KEYWORD

nonn,hard,more

AUTHOR

Richard C. Schroeppel, Oct 29 2002

EXTENSIONS

a(10)-a(12) from Ian Wanless, Dec 08 2021

STATUS

approved

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Last modified October 1 14:03 EDT 2022. Contains 357149 sequences. (Running on oeis4.)