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Number of permutations of {1, 2, ..., n} such that no k+2 points lie on a polynomial of degree k.
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%I #18 Apr 08 2018 04:36:58

%S 1,1,2,4,18,48,216,584,2870,10408,45244,160248,762554

%N Number of permutations of {1, 2, ..., n} such that no k+2 points lie on a polynomial of degree k.

%C a(n) is even for all n > 1.

%C Is this sequence strictly increasing for n > 0?

%H Programming Puzzles & Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/160382/53884">Permutations such that no k+2 points fall on any polynomial of degree k</a>

%e For n = 4, the 18 different permutations are:

%e [1,2,4,3],[1,3,2,4],[1,3,4,2],[1,4,2,3],[2,1,3,4],[2,1,4,3],

%e [2,3,1,4],[2,4,1,3],[2,4,3,1],[3,1,2,4],[3,1,4,2],[3,2,4,1],

%e [3,4,1,2],[3,4,2,1],[4,1,3,2],[4,2,1,3],[4,2,3,1],[4,3,1,2].

%Y Cf. A300002.

%K nonn,more

%O 0,3

%A _Peter Kagey_, Mar 26 2018

%E a(0) and a(10)-a(12) from _Peter J. Taylor_, Mar 28 2018