I am looking for a proof for this formula:
$$\sum_{t=1}^N\sum_{s=1}^N f(t-s) = \sum_{k=-N+1}^{N-1} (N-|k|)f(k)$$
2026-03-25 23:35:33.1774481733
proof for double summation formula
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... and from $k = 1-N$ to $N-1$.
Hint: how many pairs $(s,t)$ are there with $t-s = k$?