1,3

Equivalently, the number of isomorphism class of transitive PSL_2(ZZ) actions on a finite set of size n.

Also the number of different connected trivalent diagrams of size n.

Also the number of (r,s) pair of permutions in S_n, up to simultaneous conjugation, which generate a transitive action and for which r is involutive i.e. r^2 = id and s is of weak order three i.e. s^3 = id.

S. A. Vidal, Sur la Classification et le Denombrement des Sous-groupes du Groupe Modulaire et de leurs Classes de Conjugaison (in French), 2006, http://arXiv.org/abs/math.CO/0702223

If A(z) = g.f. of a(n) and B(z) = g.f. of A121352 then A(z) = sum_{k > 0} mu(k)/k log(B(z^k)) (Moebius inversion formula)

with(numtheory, mobius) : mu := k -> `if`( k mod 2 = 0, 2/k, 1/k ) : nu := k -> `if`( k mod 3 = 0, 3/k, 1/k ) : u := (k, n) -> add(mu(k)^(n-2*k2)/(n-2*k2)!/k2!/(2*k)^k2, k2=0..floor(n/ 2)) ; v := (k, n) -> add(nu(k)^(n-3*k3)/(n-3*k3)!/k3!/(3*k)^k3, k3=0..floor(n/ 3)) ; N := 100 # For example. add(convert(taylor(log(add(n!*k^n*u(k, n)*v(k, n)*t^(k*n), n = 0..floor (N/k))), t=0, N+1), polynom), k=1..N) : lZF := sort (%, t, ascending) : add(mobius(k)/k*rem(subs(t=t^k, lZF), t^(N+1), t), k=1..N) : sort (%, t, ascending);

Connected version of A121352.

Unlabeled version of A121355.

Cf. also A005133, A121356, A121357.

Sequence in context: A100632 A111540 A096440 this_sequence A135080 A117260 A077944

Adjacent sequences: A121347 A121348 A121349 this_sequence A121351 A121352 A121353

nonn

Samuel Alexandre Vidal (samuel.vidal(AT)free.fr), Jul 23 2006