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Yes, this will do it. Is there any reference where you found this example? Based on this, I can find other ones by guesswork, but it would be nice to find a systematic way.
Thank you Noam. The mistake was corrected. Gerald, the approximation $2^r n^r/r!$ (volume of ball in the $l_1$ norm) is good for fixed $r$ and (very) large $n$. However, when $r$ also increases (for example, if r = O(n)), what should be the behavior?
There was a mistake on the set \mbox{#} \lbrace x \in \mathbb{Z}^n : |x_1| + \cdots + |x_n| \leq r \rbrace . It now counts the number of points within the l_1 norm, indeed.
