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A239142 Number of strict partitions of n having standard deviation sigma > 1.

%I A239142 #7 Mar 14 2014 13:26:30
%S A239142 0,0,0,0,1,1,3,4,5,8,10,12,16,20,24,30,36,43,52,62,73,87,102,119,140,
%T A239142 163,189,220,254,293,338,388,445,510,583,665,758,862,979,1111,1258,
%U A239142 1423,1608,1814,2045,2302,2588,2907,3262,3656,4094,4580,5118,5715,6376
%N A239142 Number of strict partitions of n having standard deviation sigma > 1.
%C A239142 Regarding standard deviation, see Comments at A238616.
%F A239142 a(n) + A239141(n) = A000009(n) for n >=1.
%F A239142 G.f.: Product_{m>=1} (1+x^m) -1 +(x^5+x^4+x^3+2*x^2+x+1)*x / ((x-1)*(x^2+x+1)). - _Alois P. Heinz_, Mar 14 2014
%e A239142 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) = 5.
%t A239142 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]]
%t A239142 Table[Count[g[n], p_ /; s[p] < 1], {n, z}]   (* A239140 *)
%t A239142 Table[Count[g[n], p_ /; s[p] <= 1], {n, z}]  (* A239141 *)
%t A239142 Table[Count[g[n], p_ /; s[p] == 1], {n, z}]  (* periodic 01 *)
%t A239142 Table[Count[g[n], p_ /; s[p] > 1], {n, z}]   (* A239142 *)
%t A239142 Table[Count[g[n], p_ /; s[p] >= 1], {n, z}]  (* A239143 *)
%t A239142 t[n_] := t[n] = N[Table[s[g[n][[k]]], {k, 1, PartitionsQ[n]}]]
%t A239142 ListPlot[Sort[t[30]]] (*plot of st.dev's of strict partitions of 30*)
%t A239142 (* _Peter J. C. Moses_, Mar 03 2014 *)
%Y A239142 Cf. A239140, A239141, A239142, A000009, A238616.
%K A239142 nonn,easy
%O A239142 1,7
%A A239142 _Clark Kimberling_, Mar 11 2014