# How to assign Subscript[C, i] to a Sum?

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, {k}], Total[#] == 30 &]


For example, if k = 2, the results of

Select[Subsets[Range, {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!

• Your sum returns a list of size k, but it should return a number. – Coolwater Feb 28 '14 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 '14 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 '14 at 14:03
• Thanks for your advice! Could you answer my question below? – Winnie Lee Mar 1 '14 at 2:42

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: 