I don't think a user who wants to deal with such restricted-domain kinds of summations would need to understand InputForm at all, provided only that the sigma-notation form was shown. After discovering it from and InputForm expression, subsequently I used the Classroom Assistant palette as usual, but adjusting the lower- and upper-limits to conform to the discovered form.

Thanks Jim for your answers. I think it is a lot of programming effort for a facility which should be native or will be provided in future releases of MMA (they opened already a door towards what I am looking for but not much). This is more a comment than an answer.

Sorry, I wasn't trying to be facetious but was more thinking that coding (2i) and (2i+1) for even and odd integers would allow for Simplify or FullSimplify potentially to find more simplified expressions that didn't require a summation notation.

So it sounds like from the other responses that you want a simple way to input the restrictions on the indices AND have those display in a readable/visually-pleasing/standard-typesetting format (likely having $j \neq i$ placed right below $j=0$).

The only thing I can offer is something like my original comment such that your example above becomes

$$\sum _{i=0}^{10} \sum _{j=0}^5 x_i y_j-\sum _{i=0}^5 x_i y_i$$

Thanks. I do not quite understand the use of the the Makeboxes statements unless this one: If I now type

Sum[ i, {i, 0, 6,2}] //HoldForm // TraditionalForm

I retrieve my original ? expression which I have to ReleaseHold to evaluate. Correct? Does your answer also mean that you cannot natively use in MMA the traditional ? notation such as my first example without Makeboxes statements describing it with the corresponding InputForm thrown in ?

You might adapt something like this:

MakeBoxes[Sum[e_, {i_, a_, b_, 2}], TraditionalForm] := 
 RowBox[{UnderoverscriptBox["\[Sum]", 
    RowBox[{MakeBoxes[i == a, TraditionalForm], ",\[VeryThinSpace]", 
      MakeBoxes[i, TraditionalForm], " even"}], 
    MakeBoxes[b, TraditionalForm]], MakeBoxes[e, TraditionalForm]}]

MakeBoxes[Sum[e_, {i_, a_, b_, m_}], TraditionalForm] := 
 RowBox[{UnderoverscriptBox["\[Sum]", 
    RowBox[{MakeBoxes[i == a, TraditionalForm], " (mod ", 
      MakeBoxes[m, TraditionalForm], ")"}], MakeBoxes[b, TraditionalForm]], 
   MakeBoxes[e, TraditionalForm]}]

Sum[f[i], {i, 0, n, 2}] // TeXForm

(* -->  \sum _{i=0\text{,$\, $}i\text{ even}}^n f(i) *)

Sum[f[i], {i, 0, n, 3}] // TeXForm

(* --> \sum _{i=0\text{ (mod }3)}^n f(i) *)