A301802 Number of permutations of {1, 2, ..., n} such that no k+2 points lie on a polynomial of degree k.

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

Offset

0,3

Comments

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

Is this sequence strictly increasing for n > 0?

Links

Table of n, a(n) for n=0..12.

Programming Puzzles & Code Golf Stack Exchange, Permutations such that no k+2 points fall on any polynomial of degree k

Example

For n = 4, the 18 different permutations are:
[1,2,4,3],[1,3,2,4],[1,3,4,2],[1,4,2,3],[2,1,3,4],[2,1,4,3],
[2,3,1,4],[2,4,1,3],[2,4,3,1],[3,1,2,4],[3,1,4,2],[3,2,4,1],
[3,4,1,2],[3,4,2,1],[4,1,3,2],[4,2,1,3],[4,2,3,1],[4,3,1,2].

Crossrefs

Cf. A300002.

Sequence in context: A151449 A045664 A106520 * A318249 A093045 A330432

Adjacent sequences: A301799 A301800 A301801 * A301803 A301804 A301805

Keyword

nonn,more

Author

Peter Kagey, Mar 26 2018

Extensions

a(0) and a(10)-a(12) from Peter J. Taylor, Mar 28 2018

Status

approved