The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A238658 Number of partitions of n having population standard deviation < 2. 5
 1, 2, 3, 5, 7, 10, 14, 19, 25, 33, 44, 57, 72, 92, 114, 143, 179, 216, 267, 321, 389, 470, 562, 668, 798, 946, 1100, 1295, 1521, 1759, 2059, 2392, 2742, 3206, 3674, 4172, 4831, 5566, 6265, 7115, 8089, 9152, 10381, 11664, 13131, 14927, 16666, 18565, 20977 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA a(n) + A238662(n) = A000041(n). EXAMPLE There are 22 partitions of 8, whose population standard deviations are given by these approximations:  0., 3., 2., 2.35702, 1., 1.69967, 1.73205, 0., 1.24722, 0.942809, 1.22474, 1.2, 0.471405, 1., 0.707107, 0.8, 0.745356, 0., 0.489898, 0.471405, 0.349927, 0, so that a(8) = 19. MATHEMATICA z = 50; 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] < 2], {n, z}]   (* A238658 *) Table[Count[g[n], p_ /; s[p] <= 2], {n, z}]  (* A238659 *) Table[Count[g[n], p_ /; s[p] == 2], {n, z}]  (* A238660 *) Table[Count[g[n], p_ /; s[p] > 2], {n, z}]   (* A238661 *) Table[Count[g[n], p_ /; s[p] >= 2], {n, z}]  (* A238662 *) t[n_] := t[n] = N[Table[s[g[n][[k]]], {k, 1, PartitionsP[n]}]] ListPlot[Sort[t[30]]] (* plot of st deviations of partitions of 30 *) (* Second program: *) b[n_, i_, m_, s_, c_] := b[n, i, m, s, c] = If[n == 0, If[s/c - (m/c)^2 >= 4, 1, 0], If[i == 1, b[0, 0, m + n, s + n, c + n], Sum[b[n - i*j, i - 1, m + i*j, s + i^2*j, c + j], {j, 0, n/i}]]]; a[n_] := PartitionsP[n] - b[n, n, 0, 0, 0]; Array[a, 50] (* Jean-François Alcover, May 27 2021, after Alois P. Heinz *) CROSSREFS Cf. A000041, A238616, A238659, A238660, A238661, A238662. Sequence in context: A008581 A172491 A036469 * A116480 A023026 A096778 Adjacent sequences:  A238655 A238656 A238657 * A238659 A238660 A238661 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 03 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 20 10:09 EST 2022. Contains 350471 sequences. (Running on oeis4.)