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I need to calculate this summation. I have tried to solve it myself but can't seem to get anywhere.

I know that the answer needs to be $2q+1-h$.

$$\sum_{j, k=-q}^q 1_{(h+j-k=0)}$$

Jonas Dahlbæk
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user169475
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    http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference use this to improve readability of your question – Bman72 Aug 13 '14 at 10:44
  • Your notation is ambiguous, how is the summation done? – Daniel R Aug 13 '14 at 10:45
  • What if e.g. $q=1$ and $h=10$? Then every term in the summation is $0$ so the sum itself is $0$. This does not equalize $2q+1-h=-7$. Also check the edit that has been done on your question. Maybe something is wrong. – drhab Aug 13 '14 at 11:07
  • I suspect that an extra condition is needed here: $h\in\left{ 0,\dots,2q+1\right} $ – drhab Aug 13 '14 at 11:30

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Consider the matrix $A_{kj}$, $1\leq i,j \leq 2q+1$ with entries $$ A_{kj}=1_{h}(k-j). $$ Then your sum is precisely $\sum_{i,j}A_{ij}$. When $h=0$, only the diagonal is non-zero, so the sum is $2q+1$. When $h=|1|$, you get ones above the diagonal, so the sum is $2q$. When $|h|\geq 2q+1$, the sum is $0$. Can you fill in the remaining cases?

Jonas Dahlbæk
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