OFFSET
1,6
COMMENTS
Regarding standard deviation, see Comments at A238616.
FORMULA
G.f.: Product_{m>=1} (1+x^m) -1 +(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) = 5.
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 11 2014
STATUS
approved