OFFSET
1,4
COMMENTS
When n is even, the convex hull of two vertices which are opposite each other is a diameter of the circumcircle of the n-gon, and is counted as including the centroid. - Peter J. Taylor, Sep 07 2017
FORMULA
a(n) = A000029(n) - 2 - 1/2 Sum_{k=0..floor((n-3)/2)} (2^k + 2^ceiling(k/2)). - Peter J. Taylor, Sep 07 2017
EXAMPLE
For n = 5 a convex hull needs at least three vertices to contain the centroid of the pentagon. There are two convex hulls of three vertices up to symmetry, of which the "fat" triangle doesn't contain the centroid, and the "thin" triangle does. There is one convex hull of four vertices and one of five vertices up to symmetry, both of which contain the centroid. Therefore a(5) = 3.
CROSSREFS
KEYWORD
nonn
AUTHOR
J. Stauduhar, Sep 04 2017
EXTENSIONS
More terms from Peter J. Taylor, Sep 07 2017
STATUS
approved