A076021
Number of fully idempotent systems with n elements with one binary operation satisfying the equation B(AB)=A (idempotent semisymmetric quasigroups).
Original entry on oeis.org
1, 0, 1, 1, 0, 0, 4, 0, 20, 241, 0, 9801188
Offset: 1
Richard C. Schroeppel, Oct 29 2002
A076017
Number of nonisomorphic systems with n elements with one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups).
Original entry on oeis.org
1, 1, 2, 3, 4, 9, 41, 595, 26620, 3908953, 1867918845
Offset: 1
Richard C. Schroeppel, Oct 29 2002
- D. E. Knuth, The Art of Computer Programming, Vol. 4B, in preparation.
- A. Sade, Quasigroupes demi-symétriques, Ann. Soc. Sci. Bruxelles Sér. I 79 (1965), 133-143.
a(10), a(11) and comments from
Don Knuth, May 12 2005 - May 14 2005
A076019
Number of nonisomorphic commutative systems with n elements with one binary operation satisfying the equation B(AB)=A (totally-symmetric quasigroups).
Original entry on oeis.org
1, 1, 2, 2, 1, 3, 3, 13, 12, 139, 65, 25894, 24316, 92798256, 122859802, 4366600209354
Offset: 1
Richard C. Schroeppel, Oct 29 2002
A362383
Number of labeled right involutory magmas with n elements.
Original entry on oeis.org
1, 1, 4, 64, 10000, 11881376, 192699928576, 36175612601171968, 116077185312503648813056, 5817168207073186596352000000000, 5962207128673051739782035558293177368576, 119898867867315010793162270409575082620582830800896, 57436979804085599487337333419576950752550097125586310052970496
Offset: 0
-
b:= proc(n) b(n):= `if`(n<2, 1, b(n-1)+(n-1)*b(n-2)) end:
a:= n-> b(n)^n:
seq(a(n), n=0..15); # Alois P. Heinz, Apr 30 2023
-
A85[n_] := Sum[StirlingS1[n, k]*2^k*BellB[k, 1/2], {k, 0, n}];
a[n_] := A85[n]^n;
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 14 2025, after Emanuele Munarini in A85 *)
-
\\ here b(n) is A000085(n).
b(n)=sum(j=0, n\2, binomial(n, 2*j)*(2*j)!/(2^j*j!))
a(n)=b(n)^n
A350019
Number of isotopism classes containing semisymmetric Latin squares of order n.
Original entry on oeis.org
1, 1, 1, 2, 2, 7, 33, 557, 26511, 3908091, 1867909542
Offset: 1
A076020
Number of systems with n elements with one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups). This gives numbers of systems which are isomorphic to their transpose but are noncommutative.
Original entry on oeis.org
0, 0, 0, 1, 3, 6, 24, 178, 1328
Offset: 1
Richard C. Schroeppel, Oct 29 2002
A350020
Number of species containing semisymmetric Latin squares of order n.
Original entry on oeis.org
1, 1, 1, 2, 2, 7, 28, 366, 13899, 1968997, 934327507
Offset: 1
A076018
Number of systems with n elements with one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups). Isomorphic systems and systems differing by a transposition have been omitted.
Original entry on oeis.org
1, 1, 2, 3, 4, 9, 34, 393, 13980
Offset: 1
Richard C. Schroeppel, Oct 29 2002
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