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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

Table of n, a(n) for n=1..51.

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 A234273 A120939

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 October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)