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A287892 Number of unrooted unlabeled 4-cactus graphs on 3n+1 nodes. 0

%I

%S 1,1,1,3,7,25,88,366,1583,7336,34982,172384,867638,4452029,23194392,

%T 122462546,653957197,3527218134,19192275883,105248481503,581223149532,

%U 3230039198628,18053111982952,101426901301489,572554846192811,3246191706162233,18478844801342495

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

%H Andrew Howroyd, <a href="/A287892/b287892.txt">Table of n, a(n) for n = 0..500</a>

%H Maryam Bahrani and Jérémie Lumbroso, <a href="http://arxiv.org/abs/1608.01465">Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition</a>, arXiv:1608.01465 [math.CO], 2016.

%F 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.

%o (PARI) \\ Here G(n) is A287891 as vector.

%o EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

%o 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)}

%o 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

%Y Column k=4 of A332649.

%Y Cf. A003081, A287889, A287890, A287891.

%K nonn,changed

%O 0,4

%A _N. J. A. Sloane_, Jun 21 2017

%E a(0) changed and terms a(12) and beyond from _Andrew Howroyd_, Feb 18 2020

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Last modified February 21 04:38 EST 2020. Contains 332086 sequences. (Running on oeis4.)