|
| |
|
|
A111275
|
|
Number of inequivalent non-crossing partitions of n (equally spaced) points on a circle, under rotations and reflections.
|
|
2
| |
|
|
1, 2, 3, 6, 10, 24, 49, 130, 336, 980, 2904, 9176, 29432, 97356, 326399, 1111770, 3825238, 13293456, 46553116, 164200028, 582706692, 2079517924, 7458493728, 26874412064, 97241528200, 353223728624, 1287668381250, 4709805627484
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| These may be viewed as physical "amulets" (able to be turned over in space) designed with n beads on a circle, each of which is a vertex of exactly one of a set of non-touching internal polygons (which may be 1-gons (beads), 2-gons (2 connected beads), etc.).
|
|
|
REFERENCES
| S.-C. Chang, J. L. Jacobsen, J. Salas, R. Shrock, "Exact Potts model partition functions for strips of the triangular lattice", J. Statist. Phys. 114, nos.3-4, pp. 763-823 [Corollary 2.1]
Motzkin, T. "Relations Between Hypersurface Cross Ratios and a Combinatorial Formula for Partitions of a Polygon for Permanent Preponderance and for Non-Associative Products." Bull. Amer. Math. Soc. 54, page 360, 1948.
|
|
|
LINKS
| D. Callan and L. Smiley, Non-crossing Partitions under Rotation and Reflection
L. Smiley, a(6)
L. Smiley, a(5)
|
|
|
FORMULA
| (A054357(n) + A001405(n))/2.
|
|
|
MATHEMATICA
| Table[Length[EquivalenceClasses[NCPartitions[n], groupDihedral[n]]], {n, 9}]
|
|
|
CROSSREFS
| Cf. A111274.
Sequence in context: A152536 A124345 A123256 * A192440 A054357 A056606
Adjacent sequences: A111272 A111273 A111274 * A111276 A111277 A111278
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| David Callan (callan (at) stat.wisc.edu) and Len Smiley (smiley (at) math.uaa.alaska.edu), Oct 21 2005
|
| |
|
|
