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A091487 Number of unlabeled 2,3 cacti (triangular cacti with bridges). 6
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 (list; graph; refs; listen; history; text; internal format)
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: A027118 A114582 A107387 * A247332 A162092 A143884

Adjacent sequences:  A091484 A091485 A091486 * A091488 A091489 A091490

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 14 2004

STATUS

approved

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Last modified August 4 07:32 EDT 2020. Contains 336201 sequences. (Running on oeis4.)