A303835 Number of noncrossing path sets on n nodes up to rotation and reflection with isolated vertices allowed.

1, 1, 2, 3, 8, 19, 64, 212, 833, 3360, 14476, 63848, 289892, 1338000, 6275589, 29791100, 142973014, 692507861, 3382070233, 16638445745, 82395500651, 410463736691, 2055858519575, 10347925039015, 52321093290715, 265648012207312, 1353953547877556, 6925400869302520

Offset: 0

Author

Andrew Howroyd, May 01 2018

Keywords

• nonn

Examples

			Case n=3: There are 3 possibilities:
.
     o        o       o
                     / \
   o   o    o---o   o   o
.
Case n=4: There are 8 possibilities:
.
   o   o    o   o    o   o    o   o    o   o    o---o    o   o    o---o
                       /      |          /               |   |      /
   o   o    o---o    o   o    o---o    o---o    o---o    o---o    o---o
.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A303731, A303839.

Programs

PARI

\\ See A303731 for NCPathSetsModDihedral
Vec(NCPathSetsModDihedral(vector(30, k, 1)))