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Search: id:A111275
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| A111275 |
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Number of inequivalent non-crossing partitions of n (equally spaced) points on a circle, under rotations and reflections. |
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+0
3
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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.).
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REFERENCES
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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.
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LINKS
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D. Callan and L. Smiley, Non-crossing Partitions under Rotation and Reflection
L. Smiley, a(6)
L. Smiley, a(5)
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FORMULA
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(A054357(n) + A001405(n))/2.
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MATHEMATICA
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Table[Length[EquivalenceClasses[NCPartitions[n], groupDihedral[n]]], {n, 9}]
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CROSSREFS
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Cf. A111274.
Sequence in context: A122381 A124345 A123256 this_sequence A054357 A056606 A062527
Adjacent sequences: A111272 A111273 A111274 this_sequence A111276 A111277 A111278
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KEYWORD
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nonn
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AUTHOR
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David Callan (callan (at) stat.wisc.edu) and Len Smiley (smiley (at) math.uaa.alaska.edu), Oct 21 2005
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