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

0,3

Links

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

Example

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
.

Prog

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

Crossrefs

Cf. A303731, A303839.

Sequence in context: A321255 A243791 A243335 * A007999 A006609 A005663

Adjacent sequences: A303832 A303833 A303834 * A303836 A303837 A303838

Keyword

nonn

Author

Andrew Howroyd, May 01 2018

Status

approved