A287891 Number of rooted unlabeled 4-cactus graphs on 3n+1 nodes.

1, 1, 3, 11, 46, 208, 1002, 5012, 25863, 136519, 733902, 4003475, 22106155, 123313289, 693871975, 3933700703, 22447035938, 128828019447, 743142630614, 4306327193744, 25056121416684, 146325789652514, 857393585946194, 5039223717251954, 29700183601347111, 175496470696059267

Offset: 0

Author

N. J. A. Sloane, Jun 21 2017

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465 [math.CO], 2016.

Crossrefs

Column k=4 of A332648.

Cf. A003080, A287889, A287890, A287892.

Programs

PARI

EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
seq(n)={my(v=[]); for(n=1, n, my(g=1+x*Ser(v)); v=EulerT(Vec(g*(g^2 + subst(g, x, x^2))/2))); concat([1], v)} \\ Andrew Howroyd, Feb 17 2020

Extensions

a(0) changed and terms a(11) and beyond from Andrew Howroyd, Feb 17 2020