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A permutation $p$ is called antiarithmetic if there is no subsequence of it forming an arithmetic progression of length bigger than $2$, i.e. there are no three indices $0 ≤ i < j < k < n$ such that $(p_i, p_j, p_k)$ forms an arithmetic progression.

I managed to find one of the anti-arithmetic sequences. How many anti-arithmetic sequences can be there of numbers $0$ to $n$?

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This is known as a sequence, but no formula for it was in the O.E.I.S. It is described as the number of permutations of $n$ with no three term arithmetic progressions, just about how you state it, and it is sequence A003407. I think if there were any reasonable formula, or even recurrence, it would have been mentioned at OEIS. –  coffeemath Jun 3 '13 at 10:38
    
@coffeemath, Thanks, I didn't know of that sequence. –  Priyank Bhatnagar Jun 3 '13 at 10:53
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