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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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/2-1) + Sum{d|n, d<n} totient(n/d) * A002426(d)). - Andrew Howroyd, Apr 01 2017

MATHEMATICA

a1006[0] = 1; a1006[n_Integer] := a1006[n] = a1006[n-1] + Sum[a1006[k]* a1006[n -2-k], {k, 0, n-2}];

a142150[n_] := n*(1 + (-1)^n)/4;

a2426[n_] := Coefficient[(1 + x + x^2)^n, x, n];

a[0] = 1; a[n_] := (1/n)*(a1006[n]+a142150[n]*a1006[n/2-1] + Sum[EulerPhi[ n/d]*a2426[d], {d, Most @ Divisors[n]}]);

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Jul 02 2018, after Andrew Howroyd *)

CROSSREFS

Cf. A001006, A185100, A002426, A002995.

Sequence in context: A032258 A153949 A302400 * A158649 A019964 A087377

Adjacent sequences:  A175951 A175952 A175953 * A175955 A175956 A175957

KEYWORD

nonn

AUTHOR

Max Alekseyev, Oct 29 2010

STATUS

approved

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Last modified November 20 08:16 EST 2018. Contains 317385 sequences. (Running on oeis4.)