A091487 Number of unlabeled 2,3 cacti (triangular cacti with bridges).

1, 1, 2, 3, 7, 16, 41, 106, 304, 880, 2674, 8284, 26347, 85076, 279324, 928043, 3118915, 10580145, 36199094, 124774041, 432990333, 1511628113, 5306305978, 18719781786, 66342222729, 236100395649, 843490024052, 3024220006717, 10878908844745, 39255047915513

Offset

1,3

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.

Index entries for sequences related to cacti

Formula

G.f.: A(x) = B(x)-B(x)^2/2+B(x^2)/2+B(x^3)/3-B(x)^3/3 where B is g.f. of A091486.

Prog

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
b(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))))); p}
seq(n)={my(p=b(n)); Vec(p - p^2/2 - p^3/3 + subst(p, x, x^2)/2 + subst(p, x, x^3)/3)} \\ Andrew Howroyd, Aug 30 2018

Crossrefs

Cf. A091486, A091489.

Sequence in context: A114582 A352816 A107387 * A247332 A162092 A143884

Adjacent sequences: A091484 A091485 A091486 * A091488 A091489 A091490

Keyword

nonn

Author

Christian G. Bower, Jan 14 2004

Status

approved