|
%I #9 Mar 11 2023 00:13:15
%S 1,1,0,1,1,6,13,57,169,673,2301,8933,32747,127063,483484,1889957,
%T 7352241,29003446,114481435,455542880,1816976042,7285391071,
%U 29291855748,118218771203,478372112363,1941436590561,7897802784418,32205683248225,131602039333873
%N Number of noncrossing bridgeless cacti with n nodes.
%H Andrew Howroyd, <a href="/A361244/b361244.txt">Table of n, a(n) for n = 0..500</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cactus_graph">Cactus graph</a>.
%H <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>.
%F G.f. 1 + A(x) where A(x) satisfies A(x) = x^2*(x - A(x)^2)/(x^2 - x*A(x)^2 - A(x)^4).
%o (PARI) seq(n)={my(g=1+O(x)); for(n=1, n\2, g=1/(1 - x^2*g^4/(1 - x*g^2))); Vec(1 + x*g + O(x*x^n))}
%Y Cf. A003168, A361242, A361245.
%K nonn
%O 0,6
%A _Andrew Howroyd_, Mar 08 2023
|
