A361244 Number of noncrossing bridgeless cacti with n nodes.

1, 1, 0, 1, 1, 6, 13, 57, 169, 673, 2301, 8933, 32747, 127063, 483484, 1889957, 7352241, 29003446, 114481435, 455542880, 1816976042, 7285391071, 29291855748, 118218771203, 478372112363, 1941436590561, 7897802784418, 32205683248225, 131602039333873

Offset: 0

Author

Andrew Howroyd, Mar 08 2023

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• Wikipedia, Cactus graph.
• Index entries for sequences related to cacti.

Crossrefs

Cf. A003168, A361242, A361245.

Programs

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))}

Formula

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).