

A175954


Unlabeled (cyclic) Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n unlabeled points equally spaced on a circle, up to rotations of the circle.


3



1, 1, 2, 2, 4, 5, 12, 19, 46, 95, 230, 528, 1320, 3219, 8172, 20714, 53478, 138635, 363486, 957858, 2543476, 6788019, 18218772, 49120019, 133036406, 361736109, 987316658, 2703991820, 7429445752, 20473889133, 56579632732, 156766505691
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OFFSET

0,3


COMMENTS

Unlabeled version of A001006.
The number of such chord configurations on 2n vertices with n chords is given by A002995(n+1).


LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200
Andrew Howroyd, Chord Configuration Symmetries


FORMULA

For odd prime p, a(p) = (A001006(p)  1)/p + 1.
a(n) = (1/n) * (A001006(n) + A142150(n) * A001006(n/21) + Sum{dn, d<n} totient(n/d) * A002426(d)).  Andrew Howroyd, Apr 01 2017


CROSSREFS

Cf. A001006, A185100, A002426, A002995.
Sequence in context: A103420 A032258 A153949 * A158649 A019964 A087377
Adjacent sequences: A175951 A175952 A175953 * A175955 A175956 A175957


KEYWORD

nonn


AUTHOR

Max Alekseyev, Oct 29 2010


STATUS

approved



