A292276 - OEIS

A292276

a(n) = number of vertices of the convex hull of the set of points of norm <= n^2 in square lattice.

1, 4, 4, 8, 12, 12, 12, 12, 20, 12, 20, 20, 20, 20, 20, 20, 20, 24, 28, 20, 20, 20, 36, 36, 28, 20, 36, 36, 36, 36, 28, 36, 36, 36, 44, 36, 36, 36, 36, 52, 44, 36, 36, 36, 52, 44, 52, 52, 44, 52, 44, 60, 52, 44, 52, 44, 52, 52, 52, 52, 60, 52, 52, 52, 68, 44

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

The convex hull of a finite point set in dimension 2, say S, forms a convex polygon whose vertices are in S.

For any n >= 0, A000328(n) gives the number of elements of the set of points of norm <= n^2 in square lattice.

For symmetry reasons, a(n) is a multiple of 4 for any n > 0.

LINKS

Table of n, a(n) for n=0..65.

Rémy Sigrist, C++ program for A292276

Rémy Sigrist, Illustration of the convex hulls for n=0..10

Wikipedia, Convex hull of a finite point set