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A175954
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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.
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4
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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
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0,3
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COMMENTS
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The number of such chord configurations on 2n vertices with n chords is given by A002995(n+1).
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LINKS
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FORMULA
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For odd prime p, a(p) = (A001006(p) - 1)/p + 1.
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MATHEMATICA
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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]}]);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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