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

Offset: 0

Author

Rémy Sigrist, Sep 13 2017

Keywords

• nonn

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.

Examples

			See Links section.
		

Links

• 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

Crossrefs

Cf. A000328, A046109.