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Permutations are arrangements of the numbers $1,\ldots,n$ in an arbitrary order.

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Permuting natural numbers

Now we have to find total number of permutations of this sequence such that the sum of any two adjacent numbers is $ \le k$ ( $z \leq 10^6$, $\;\;z < k < 2*z$ ) Here is what I have been able to think …
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