A091488 Number of asymmetric rooted 2,3 cacti (triangular cacti with bridges).

1, 1, 1, 3, 6, 16, 42, 115, 319, 909, 2614, 7622, 22422, 66556, 198946, 598617, 1811205, 5508015, 16825307, 51605568, 158860950, 490666293, 1520106655, 4722502437, 14708971581, 45921804883, 143682973435, 450477673623

Offset: 1

Author

Christian G. Bower, Jan 14 2004

Keywords

• nonn
• eigen

Comments

Also asymmetric involution rooted trees.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• N. J. A. Sloane, Transforms
• Index entries for sequences related to cacti
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A091486, A091489.

Programs

PARI

WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}
seq(n)={my(p=O(x)); for(n=1, n, p=x+x^2*(Ser(WeighT(Vec(p + (p^2 - subst(p,x,x^2))/2))))); Vec(p)} \\ Andrew Howroyd, Aug 30 2018

Formula

Shifts left under transform T where Ta = WEIGH(W_1, 2(a)). W_1, 2(a) has g.f. A(x)+(A(x^2)-A(x)^2)/2.