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A361243 Number of nonequivalent noncrossing cacti with n nodes up to rotation and reflection. 3
1, 1, 1, 2, 5, 17, 79, 421, 2537, 16214, 108204, 743953, 5237414, 37574426, 273889801, 2023645764, 15128049989, 114256903169, 870786692493, 6690155544157, 51771411793812, 403238508004050, 3159259746188665, 24884525271410389, 196966954270163612 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A020096 A362109 A187245 * A302194 A289739 A243337
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Mar 07 2023
STATUS
approved

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Last modified May 23 01:37 EDT 2024. Contains 372758 sequences. (Running on oeis4.)