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 A269800 Convolution of A000107 and A027852. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. LINKS 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. MATHEMATICA 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 *) CROSSREFS Cf. A000107, A027852. Sequence in context: A026327 A014531 A062107 * A033113 A360714 A290718 Adjacent sequences: A269797 A269798 A269799 * A269801 A269802 A269803 KEYWORD nonn AUTHOR R. J. Mathar, Mar 05 2016 STATUS approved

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Last modified March 20 11:03 EDT 2023. Contains 361375 sequences. (Running on oeis4.)