A076016
Number of systems with n elements having one binary operation satisfying the equation B(AB)=A (semisymmetric quasigroups).
Original entry on oeis.org
1, 2, 3, 18, 120, 2880, 140256, 20782080, 9569532672, 14175610675200, 74559788174868480
Offset: 1
Richard C. Schroeppel, Oct 29 2002
A362382
Number of nonisomorphic right involutory magmas with n elements.
Original entry on oeis.org
1, 1, 3, 16, 475, 100666, 267954164, 7178089200724, 2878905036230723360, 16030557330452794172050567, 1643024454743084814743097053747492, 3003719433250221394022136941323628209106412, 119909786948816191249293422143299520925389900896422044
Offset: 0
-
B(c,k)=sum(j=0, c\2, if(k%2, 1, 2^(c-2*j))*k^j*binomial(c, 2*j)*(2*j)!/(2^j*j!))
K(v)=my(S=Set(v)); prod(i=1, #S, my(k=S[i], c=#select(t->t==k, v)); B(c,k))
R(v,m)=concat(vector(#v,i,my(t=v[i], g=gcd(t,m)); vector(g, i, t/g)))
a(n)={my(s=0); forpart(p=n, my(v=Vec(p), S=Set(v)); s+=prod(i=1, #S, my(m=S[i], c=#select(t->t==m, v)); (K(R(v,m))/m)^c/c!)); s}
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
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
Showing 1-4 of 4 results.
Comments