A362382 Number of nonisomorphic right involutory magmas with n elements.

1, 1, 3, 16, 475, 100666, 267954164, 7178089200724, 2878905036230723360, 16030557330452794172050567, 1643024454743084814743097053747492, 3003719433250221394022136941323628209106412, 119909786948816191249293422143299520925389900896422044

Offset

0,3

Comments

A magma with element set X is right involutory if (xy)y = x for x,y in X.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..40

Prog

(PARI)
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}

Crossrefs

Cf. A001329 (magmas), A076017, A076019, A361720, A362383 (labeled).

Sequence in context: A081782 A176299 A081780 * A297118 A002794 A132559

Adjacent sequences: A362379 A362380 A362381 * A362383 A362384 A362385

Keyword

nonn

Author

Andrew Howroyd, Apr 17 2023

Status

approved