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A111275 Number of inequivalent non-crossing partitions of n (equally spaced) points on a circle, under rotations and reflections. 8
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; text; internal format)
OFFSET

1,2

COMMENTS

These may be viewed as bracelets (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

Table of n, a(n) for n=1..28.

D. Callan and L. Smiley, Non-crossing Partitions under Rotation and Reflection

Tilman Piesk, Partition related number triangles

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. A209612.

Sequence in context: A185164 A124345 A123256 * A298537 A272079 A212606

Adjacent sequences:  A111272 A111273 A111274 * A111276 A111277 A111278

KEYWORD

nonn

AUTHOR

David Callan and Len Smiley, Oct 21 2005

STATUS

approved

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Last modified November 17 12:09 EST 2018. Contains 317276 sequences. (Running on oeis4.)