OFFSET
0,4
COMMENTS
A noncrossing cactus is a connected noncrossing graph (A007297) that is a cactus graph (a tree of edges and polygons).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
Wikipedia, Cactus graph.
EXAMPLE
The a(4) = 5 nonequivalent cacti have the following blocks:
{{1,2}, {1,3}, {1,4}},
{{1,2}, {1,3}, {3,4}},
{{1,2}, {1,4}, {2,3}},
{{1,2}, {1,3,4}},
{{1,2,3,4}}.
Graphically these can be represented:
1---4 1 4 1---4 1---4 1---4
| \ | \ | | | \ | | |
2 3 2 3 2---3 2 3 2---3
PROG
(PARI) \\ Here F(n) is the g.f. of A003168.
F(n) = {1 + serreverse(x/((1+2*x)*(1+x)^2) + O(x*x^n))}
seq(n) = {my(f=F(n-1)); Vec(1/(1 - x*subst(f + O(x^(n\2+1)), x, x^2)) + 1 + intformal(f) - sum(d=2, n, eulerphi(d) * log(1-subst(x*f^2 + O(x^(n\d+1)), x, x^d)) / d), -n-1)/2}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Mar 07 2023
STATUS
approved