cp's OEIS Frontend

A111275 Number of inequivalent non-crossing partitions of n (equally spaced) points on a circle, under rotations and reflections.

%I A111275 #17 Oct 31 2015 14:01:38
%S A111275 1,2,3,6,10,24,49,130,336,980,2904,9176,29432,97356,326399,1111770,
%T A111275 3825238,13293456,46553116,164200028,582706692,2079517924,7458493728,
%U A111275 26874412064,97241528200,353223728624,1287668381250,4709805627484
%N A111275 Number of inequivalent non-crossing partitions of n (equally spaced) points on a circle, under rotations and reflections.
%C A111275 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.).
%D A111275 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]
%D A111275 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.
%H A111275 D. Callan and L. Smiley, <a href="http://arXiv.org/abs/math.CO/0510447">Non-crossing Partitions under Rotation and Reflection</a>
%H A111275 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Partition_related_number_triangles#rotref">Partition related number triangles</a>
%H A111275 L. Smiley, <a href="http://www.math.uaa.alaska.edu/~smiley/nc/6pointNCPP.pdf">a(6)</a>
%H A111275 L. Smiley, <a href="http://www.math.uaa.alaska.edu/~smiley/nc/10NC.pdf">a(5)</a>
%F A111275 (A054357(n) + A001405(n))/2.
%t A111275 Table[Length[EquivalenceClasses[NCPartitions[n], groupDihedral[n]]], {n, 9}]
%Y A111275 Cf. A209612.
%K A111275 nonn
%O A111275 1,2
%A A111275 _David Callan_ and _Len Smiley_, Oct 21 2005