A091486 Number of unlabeled rooted 2,3 cacti (triangular cacti with bridges).

1, 1, 3, 7, 21, 60, 190, 600, 1977, 6589, 22408, 77050, 268178, 941599, 3333585, 11882427, 42615480, 153653039, 556664752, 2025330509, 7397242875, 27111563026, 99681629658, 367563272278, 1358945378906, 5036549490009, 18708739990129, 69640873691941

Offset

1,3

Comments

Also number of unlabeled involution rooted trees.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465 [math.CO], 2016.

N. J. A. Sloane, Transforms

Index entries for sequences related to cacti

Index entries for sequences related to rooted trees

Formula

Shifts left under transform T where Ta = EULER(E_1, 2(a)). E_1, 2(a) has g.f. A(x)+(A(x^2)+A(x)^2)/2.

Prog

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

Crossrefs

Cf. A091487, A091488.

Sequence in context: A035080 A229188 A345955 * A056779 A183113 A102877

Adjacent sequences: A091483 A091484 A091485 * A091487 A091488 A091489

Keyword

nonn,eigen

Author

Christian G. Bower, Jan 14 2004

Status

approved