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What I want to show is:

Plot3D[
  Sum[1000*Subscript[C, i]^2/(1000*Subscript[C, i] - 600)^r, {i, 1, k}],
  {k, 1, 30}, {r, 0.1, 1.5}]

And, I want the list of Subscript[C, i] to be the elements of the subsets:

Select[Subsets[Range[30], {k}], Total[#] == 30 &]

For example, if k = 2, the results of

Select[Subsets[Range[30], {2}], Total[#] == 30 &]

is

{{1, 29}, {2, 28}, {3, 27}, {4, 26}, {5, 25}, {6, 24}, {7, 23}, {8, 
  22}, {9, 21}, {10, 20}, {11, 19}, {12, 18}, {13, 17}, {14, 16}}

Further, I want to assign {1, 29} to C1 and C2 of Sum firstly, and then assign {2, 28} to C1 and C2 of Sum secondly, etc. As a result, I will be able to get the graphic I want by Plot3D!

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Your sum returns a list of size k, but it should return a number. –  Coolwater Feb 28 at 13:05
    
Thanks for your comment! Because I want to observe a range of sum by plot3D... How can I solve this problem? –  Winnie Lee Feb 28 at 13:10
    
Don't use C as a variable name (it is a built-in function). Also, it will be easier to use a list of the cs rather than subscripts. Subscript is best thought of as a typesetting function. –  bill s Feb 28 at 14:03
    
Thanks for your advice! Could you answer my question below? –  Winnie Lee Mar 1 at 2:42
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1 Answer 1

I suspect based on this and your other related questions you want to visualize how the number of permutations of partitions of an integer total of size k changes with total and k. (If not, comment and I'll delete this answer).

If so, something like:

ListPlot3D[
 Flatten[Table[{total, k, 
    Length[Join @@ 
      Permutations /@ IntegerPartitions[total, {k}]]}, {total, 1, 
    30}, {k, 1, 8}], 1], PlotRange -> All, 
 AxesLabel -> {"Total", "K", "# of perms"}, ImageSize -> 500]

Which outputs:

enter image description here

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