A287892 Number of unrooted unlabeled 4-cactus graphs on 3n+1 nodes.

1, 1, 1, 3, 7, 25, 88, 366, 1583, 7336, 34982, 172384, 867638, 4452029, 23194392, 122462546, 653957197, 3527218134, 19192275883, 105248481503, 581223149532, 3230039198628, 18053111982952, 101426901301489, 572554846192811, 3246191706162233, 18478844801342495

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 A332649.

Cf. A003081, A287889, A287890, A287891.

Programs

PARI

\\ Here G(n) is A287891 as vector.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
G(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)}
seq(n)={my(p=Ser(G(n))); my(g(d)=subst(p,x,x^d)); Vec(g(1) + x*(2*g(4) + 3*g(2)^2 - 2*g(1)^2*g(2) - 3*g(1)^4)/8)} \\ Andrew Howroyd, Feb 18 2020

Formula

G.f.: g(x) + x*(2*g(x^4) + 3*g(x^2)^2 - 2*g(x)^2*g(x^2) - 3*g(x)^4)/8 where g(x) is the g.f. of A287891.

Extensions

a(0) changed and terms a(12) and beyond from Andrew Howroyd, Feb 18 2020