A030129
Number of nonisomorphic Steiner triple systems (STS's) S(2,3,n) on n points.
Original entry on oeis.org
1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 80, 0, 0, 0, 11084874829, 0, 14796207517873771
Offset: 1
- L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 304.
- CRC Handbook of Combinatorial Designs, 1996, p. 70.
- Daniel Heinlein and Patric R. J. Östergård, Enumerating Steiner Triple Systems, arXiv:2303.01207 [math.CO], 2023.
- Petteri Kaski and Patric R. J. Östergård (Patric.Ostergard(AT)hut.fi), The Steiner triple systems of order 19.
- Petteri Kaski and Patric R. J. Östergård, The Steiner triple systems of order 19, Mathematics of Computation, Vol. 73, No. 248 (Oct., 2004), pp. 2075-2092.
- Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Des. 30 (2022), 105-130.
- Eric Weisstein's World of Mathematics, Steiner Triple System.
- Index entries for sequences related to Steiner systems.
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}
A350025
Number of totally symmetric Latin squares of order n.
Original entry on oeis.org
1, 2, 3, 16, 30, 480, 1290, 163200, 471240, 386400000, 2269270080, 12238171545600, 149648961369600, 8089070513113497600, 160650421233958656000, 91361407076595590705971200
Offset: 1
A350026
Number of species containing totally symmetric Latin squares of order n.
Original entry on oeis.org
1, 1, 1, 2, 1, 2, 3, 13, 8, 139, 65, 25888, 24316, 92798256, 122859796
Offset: 1
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