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A111276 Number of chiral non-crossing partition patterns of n points on a circle, divided by 2. 0
0, 0, 0, 0, 0, 4, 14, 60, 210, 728, 2442, 8252, 27716, 93924, 319964, 1098900, 3800928, 13244836, 46460738, 164015272, 582353976, 2078812492 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Half of the number of those rotation-inequivalent patterns of non-crossing partitions of n (equally spaced) points on a circle which are not invariant under reflections. Division by two counts one pattern from each chiral (Right-handed,Left-handed) pair.

LINKS

Table of n, a(n) for n=1..22.

D. Callan and L. Smiley, Non-crossing Partitions under Rotation and Reflection, arXiv:math/0510447 [math.CO], 2005.

L. Smiley, a(5) = 0

L. Smiley, a(6)=8/2=4

FORMULA

a(n) = (A054357(n) - A001405(n))/2.

MATHEMATICA

a[n_] := If[n < 6, 0, ((Binomial[2n, n]/(n+1) + DivisorSum[n, Binomial[2#, #] EulerPhi[n/#] Boole[# < n]&])/n - Binomial[n, Floor[n/2]])/2];

Array[a, 22] (* Jean-François Alcover, Feb 17 2019 *)

CROSSREFS

Cf. A001405, A054357, A111275.

Sequence in context: A149492 A307488 A241706 * A149493 A299926 A307399

Adjacent sequences:  A111273 A111274 A111275 * A111277 A111278 A111279

KEYWORD

nonn,more

AUTHOR

David Callan and Len Smiley, Oct 21 2005

STATUS

approved

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)