OFFSET
0,4
COMMENTS
The number of all noncrossing trees with n edges is given by A001764.
The number of nodes will be n + 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
M. Noy, Enumeration of noncrossing trees on a circle, Discrete Math., 180, 301-313, 1998.
FORMULA
EXAMPLE
Case n=3:
o---o o---o o---o
| | \ \
o---o o o o---o
In total there are 3 distinct noncrossing trees up to rotation and reflection.
MATHEMATICA
a[n_] := (If[OddQ[n], 3*Binomial[(1/2)*(3*n - 1), (n - 1)/2], Binomial[3*n/2, n/2]] + Binomial[3*n, n]/(2*n + 1))/(2*(n + 1));
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Dec 27 2017, after Andrew Howroyd *)
PROG
(PARI) a(n)={(binomial(3*n, n)/(2*n+1) + if(n%2, 3*binomial((3*n-1)/2, (n-1)/2), binomial(3*n/2, n/2)))/(2*(n+1))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 14 2017
STATUS
approved