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 A239140 Number of strict partitions of n having standard deviation σ < 1. 5
 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Regarding standard deviation, see Comments at A238616. LINKS Index entries for linear recurrences with constant coefficients, signature (-1, 0, 1, 1). FORMULA a(n + 3) = A087039 (n) for n >= 1 (periodic with period 6); a(n) + A239143(n) = A000009(n) for n >=1. G.f.: -(x^6+x^5+x^4+2*x^3+3*x^2+2*x+1)*x / ((x-1)*(x+1)*(x^2+x+1)). - Alois P. Heinz, Mar 14 2014 EXAMPLE The standard deviations of the strict partitions of 9 are 0., 3.5, 2.5, 1.5, 2.16025, 0.5, 1.63299, 0.816497, so that a(9) = 3. MATHEMATICA z = 30; g[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; s[t_] := s[t] = Sqrt[Sum[(t[[k]] - Mean[t])^2, {k, 1, Length[t]}]/Length[t]] Table[Count[g[n], p_ /; s[p] < 1], {n, z}]   (* A239140 *) Table[Count[g[n], p_ /; s[p] <= 1], {n, z}]  (* A239141 *) Table[Count[g[n], p_ /; s[p] == 1], {n, z}]  (* periodic 01 *) Table[Count[g[n], p_ /; s[p] > 1], {n, z}]   (* A239142 *) Table[Count[g[n], p_ /; s[p] >= 1], {n, z}]  (* A239143 *) t[n_] := t[n] = N[Table[s[g[n][[k]]], {k, 1, PartitionsQ[n]}]] ListPlot[Sort[t[30]]] (*plot of st.dev's of strict partitions of 30*) (* Peter J. C. Moses, Mar 03 2014 *) Join[{1, 1, 2}, LinearRecurrence[{-1, 0, 1, 1}, {1, 2, 2, 2}, 83]] (* Ray Chandler, Aug 25 2015 *) CROSSREFS Cf. A239141, A239142, A239143, A000009, A238616. Column k=0 of A239228. Sequence in context: A118824 A209402 A082641 * A138553 A069016 A211270 Adjacent sequences:  A239137 A239138 A239139 * A239141 A239142 A239143 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 11 2014 STATUS approved

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Last modified June 24 05:39 EDT 2019. Contains 324318 sequences. (Running on oeis4.)