A156831 Let a(n) = the number of permutations (p(1),p(2),p(3)...,p(n)) of (1,2,3,...,n) where, if each (m,p(m)) is plotted on a graph, then the entire set P of the n of these plotted points would be on the perimeter of the convex hull of P.

1, 2, 6, 20, 66, 188, 466, 1022, 2098, 4032, 7342, 13090, 22726, 38824, 65286, 108902, 179762

Offset

1,2

Comments

Three points that are consecutive along the perimeter of the convex hull may be along the same line, in some of the permutations that are counted.

The first 8 terms were calculated by W. Edwin Clark. The first 17 terms were calculated by Jan Kristian Haugland, and posted to the Usenet group sci.math.

Links

Table of n, a(n) for n=1..17.

Example

For n=5, (p(1),p(2),p(3),p(4),p(5)) = (1,3,5,2,4) would be included in the count, but (1,4,3,2,5) would not because point (3,3) is not on the perimeter of the convex hull of P.

Crossrefs

Sequence in context: A148473 A000718 A148474 * A027061 A279460 A096487

Adjacent sequences: A156828 A156829 A156830 * A156832 A156833 A156834

Keyword

more,nonn

Author

Leroy Quet, Feb 16 2009

Status

approved