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0, 0, 1, 3, 10, 30, 91, 268, 790, 2308, 6737, 19609, 57044, 165796, 481823, 1400028, 4068577, 11825459, 34380152, 99981942, 290854486, 846397344, 2463892294, 7174933683, 20900764811, 60904875999, 177535250815, 517673673674, 1509950058629, 4405547856394, 12857716906991
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OFFSET
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0,4
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COMMENTS
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This counts the arrangements of n nested circles in the plane where one pair of circles touches. a(2)=1 because the (only) pair must touch. a(3)=3 because either the third circle circumscribes the touching pair or is inside one of the touching circles or is entirely separated from the touching pair.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..500
R. J. Mathar, Topologically distinct sets of non-intersecting circles in the plane, arXiv:1603.00077 [math.CO](2016), row sums Table 8.
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MATHEMATICA
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b[0] = 0; b[1] = 1; b[n_] := b[n] =Sum[Sum[d b[d], {d, Divisors[j]}] b[n - j], {j, 1, n - 1}]/(n - 1);
a7[n_] := a7[n] = b[n] + Sum[ a7[n - i] b[i], {i, 1, n - 1}];
c[n_] := c[n] = If[n <= 1, n, (Sum[Sum[d c[d], {d, Divisors[j]}] c[n - j], {j, 1, n - 1}])/(n - 1)];
a52[n_] := (Sum[c[i] c[n-i], {i, 0, n}] + If[Mod[n, 2] == 0, c[n/2], 0])/2;
a[n_] := Sum[a7[k] a52[n - k + 1], {k, 0, n + 1}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 16 2018, after Alois P. Heinz in A000107 and A027852 *)
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CROSSREFS
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Cf. A000107, A027852.
Sequence in context: A026327 A014531 A062107 * A033113 A360714 A290718
Adjacent sequences: A269797 A269798 A269799 * A269801 A269802 A269803
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KEYWORD
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nonn
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AUTHOR
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R. J. Mathar, Mar 05 2016
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STATUS
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approved
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