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 A238656 Number of partitions of n having standard deviation σ > 4. 3
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 4, 5, 9, 14, 19, 28, 41, 57, 80, 109, 149, 199, 265, 351, 457, 599, 780, 1011, 1299, 1664, 2121, 2682, 3377, 4252, 5345, 6660, 8279, 10277, 12733, 15596, 19245, 23556, 28761, 35066, 42723, 51615, 62657, 75494, 90978 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS Regarding "standard deviation" see Comments at A238616. LINKS EXAMPLE There are 30 partitions of 9, whose standard deviations are given by these approximations: 0., 3.5, 2.5, 2.82843, 1.5, 2.16025, 2.16506, 0.5, 1.63299, 1.41421, 1.63936, 1.6, 1.41421, 0.816497, 1.29904, 1.08972, 1.16619, 1.11803, 0., 0.829156, 0.979796, 0.433013, 0.748331, 0.763763, 0.699854, 0.4, 0.5, 0.451754, 0.330719, 0, so that a(9) = 0. MATHEMATICA z = 53; g[n_] := g[n] = IntegerPartitions[n]; c[t_] := c[t] = Length[t]; s[t_] := s[t] = Sqrt[Sum[(t[[k]] - Mean[t])^2, {k, 1, c[t]}]/c[t]] Table[Count[g[n], p_ /; s[p] > 3], {n, z}] (*A238655*) Table[Count[g[n], p_ /; s[p] > 4], {n, z}] (*A238656*) Table[Count[g[n], p_ /; s[p] > 5], {n, z}] (*A238657*) t[n_] := t[n] = N[Table[s[g[n][[k]]], {k, 1, PartitionsP[n]}]] ListPlot[Sort[t[30]]] (*plot of st dev's of partitions of 30*) CROSSREFS Cf. A238616, A238661, A238655, A238657. Sequence in context: A129282 A073153 A073154 * A077882 A351293 A234273 Adjacent sequences: A238653 A238654 A238655 * A238657 A238658 A238659 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 03 2014 STATUS approved

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Last modified February 3 01:46 EST 2023. Contains 360024 sequences. (Running on oeis4.)